To unlock the Genius trophy in The Bridge, you need to you will first have to complete the four main chapters of the game and unlock the "first" ending:
You can either enter the Mirror World outside the house by the tree, or you can enter the Mirror World inside each of the Chapter corridors. You need to interact with the white wire frame box to switch between the Standard and Mirror Worlds.Chapter IV-I: Mirrored Veil
Rotate with LT a little to get the Menace to roll right into the little alcove next to it. Walk right into the Veil and then rotate the level with LT until the door is upside down, and the "G" of the Menace trap is tilted slightly to one side. Come out of the Veil and head to the door. Here's the trick; you need to use momentum to flip the Menace out of its trap and onto the lower platform with the Veil, dropping right of the Professor. The trick will be finding the sweet spot where Menace will drop off the upper platform but the Professor doesn't slip off the edge of the world by the door. It'll take a few tries to get right and you might want to consider slightly adjusting the angle behind the Veil if you are really having trouble. Once you have Menace on the bottom platform you just need to carefully roll it towards the button beyond the Veil while keeping the Professor in place by the door, ready to exit as soon as the Button is pressed.Chapter IV-II: Mirrored Rook
Rotate/walk left and use Door IV. Now go right, past Door II and into the Veil. Now rotate with LT until both the Menace and the key (barely visible, non-interactive) end up by Door I, which is the non-interactive door to the right of the Veil. You need to try and grab that key shortly without getting hit by the Menace so make sure Menace is rolling under its own momentum far enough away to grab the key. Go left and use Door II, then head right and use Door I while the Menace is rolled away from it; activating Door I should make the key solidify and the Professor will grab it. Get away from the Menace. Walk back to Door II but don't use it, we're just creating some distance. Now rotate the level around so that the Professor heads to Door III. Use Door III and the other Key will appear but immediately get sucked into a new Vortex. Walk the Professor into the Vortex to pick up the key.
Rotate with RT so that the invisible Menace rolls onto the equally invisible button, freeing the Professor. Now head right until you get to Door I. Use that then use the exit door.Chapter IV-III: Mirrored Bend
Another odd level out: This time there is a hidden area which automatically inverts the Professor; there's no visible inversion point.
Keep heading left and eventually the Black Professor will disappear and the White Professor will emerge near the White door. Use it to spawn a Veil. Now head back right until you are the Black Professor. Keep going right until Black reaches the Veil. Get in the Veil and rotate with RT, until the door is pointing a little south of south-west, and the lantern in the lower left of the screen is pretty much pointing at the button (for reference, both the stationary and the swinging lantern currently visible should be pointing towards the Button, with Menace rolling around right at the bottom of the screen. This indicates that the Menace will end up on the button at the right moment. Walk left all the way until you reach Door II, which should be unlocked if Menace is on the button (go back and adjust the Veil position if this doesn't happen). Open Door II and grab the key that appears. Now you need to walk a long way left until the Black professor is in front of the black door to exit. You'll become the White professor during this journey, just keep walking and eventually the Black Professor will be in front of the exit door, with Menace on the button to unlock it.Chapter IV-IV: Mirrored Triad
This is another pain, especially to describe. Focus on one Professor at a time, that's crucial as their perspectives and their colours will keep shifting.
There are three sections which we'll name Black Key, Menace and White Key. Familiarise yourself with those sections as it's about to get confusing.
Walk the Top Professor over to the Inversion to his left and use it. Now you have a White and Black Professor in the same section, the White Key Section. Pull RT so that the White Professor is standing on a flat surface at the bottom of the screen, white key to his left on the incline. If you walk around a bit you can see that White Professor is on the floor and Black is on the ceiling, moving in opposite directions.
Focus on Black now. He's upside down, so remember his movements are inverted. Push left to move him right to the Inversion point in the right corner of this section. He'll now be White in the Black Key Section. Rotate so that White in the Black Key section walks past the white door and onto the next surface, allowing him to use the Inversion point.
Now you have Black in the Menace Section. The Menace is white so Black is currently safe -- so it's time to re-position the White Professor in the White Key Section, ignoring the Black Professor in the Menace Section. Walk/Rotate White around so that he is upside-down on the ceiling of his section (the White Key will be dangling upwards); push left to walk him right to the Inversion in the corner. (the same Inversion you used to get Black out of this section). So you now have a Black Professor in the Black Key section.
Back to the Black Professor in the Menace Section. Rotate the level so that the Menace is on the ceiling and the Black Professor is on the floor beneath it. Walk him left through the nearest Inversion. This puts a White Professor with the White Key, and Black Professor with the Black Key. One problem solved; now we need them to walk past the Keys at the same time to pick them up.
Rotate the level so that Black Key is stretched towards the white door at the top of the level, as far as it can reach on its chain. Tip LT so that the White Professor falls into the corner nearest the White Key (he'll be hidden by the Inversion pretty much) and so that the Black Professor, upside-down, has a flat surface across the top of the screen to walk to the right corner. Remember, he's upside-down; push LEFT to get the Black Professor all the way to the right-hand corner, by the inversion.
Now you should have the White Professor hidden behind an Inversion near the white key at the bottom of the screen, with the Black Professor hidden behind an Inversion at the centre-top of the screen. The key here is to tip RT so that Black and White both sail past their keys at the same time. Some say that you should push LEFT as you start to tip RT to slow the Black Professor down; I actually found the opposite to be true, and pushed RIGHT once the Black Professor started to fall. Either way you need a firm pull on RT to get them both moving at the same time. This is super tricky to pull off, the game is not very forgiving at this point, so just persevere with slightly different movements and tweaks and try not to get frustrated and lose your place. Rewind is your friend.
Assuming you now have both keys, you now need to get both Professors to be White and each in front of an exit door. Start with White in the White Key section. Send him through his left-side Inversion to put him in the Menace section. He'll be Black now, so he's safe. With the Black Professor in the Black Key section, head to the Inversion linking to the White Key Section (he should already be pretty much on top of it) and use it. You now have Black in the Menace section and White in the White Key section.
Move the Black Professor in the Menace section over to the Inversion which will flip him into the Black Key Section. Now you have a White Professor in both of the non-Menace sections, so it should just be a matter of flipping the level so that both doors are upright and walking the two Professors to their doors. You may have to do some slight tweaking and stepping to get them both in front of the doors at the same time.
Phew!Chapter IV-V: Mirrored Intersection
Luckily we don't have to do this one without walking for a trophy this time, so it's easier than before. It's still pretty mind-bending.
Rotate with LT so that the Professor lands in the Veil (upright, so he doesn't tip out of it. You want the two Menaces to carefully ease their way up so they both land on the button, so just slight pulls with LT should do it while the Professor is in the Veil.
Now you want to rotate the level, while the Professor is still Veiled, so that the two moving lanterns are each pointing roughly towards each button. The top right lantern should be pointing at the Button with the Menaces on it, currently in the south, while the left Lantern should be vaguely pointing towards the left button (its long chain means that it actually extends past the button, but the chain should be "crossing" the button; if it helps, position the left lantern so that it's pretty much pointing left; the lantern is touching the key symbol underneath the button).
Now walk left out of the veil. You now want to rotate carefully so that both Menaces end up down by the exit door, so again just little careful pulls of LT so that neither Menace overshoots. The Professor should be positioned upright on a small horizontal ledge to the upper right, while the Menaces, piled up by the door, are pointed towards the top left corner of the screen.
This next bit is a little tricky. You want to tip a bit with LT so that one Menace heads towards the bottom button, while the other Menace flies towards the surface directly above the Professor's head. As soon as you're sure the Menaces are headed the right way, pull harder with LT so that Professor does a limbo underneath the Menace flying up towards him. Now make sure that the Professor tips down towards the door. Now you have the Professor ready to leave, one Menace on the button at the top of the screen and the other Menace over on the left. You now need to sharply pull LT so that the left-hand Menace falls forcefully enough to end up all the way over on the right, hitting the other button and allowing the Professor to escape. (If the door doesn't open, you might need to apply a little more momentum to the right-hand Menace to get it to fully push the button, and quickly escape before it bounces back off).Chapter IV-VI: Mirrored Archway
Another pretty tricky one to explain.
Walk right and tilt RT all the way around until eventually the Arch is pointing south and the Professor is standing on the sliding platform. Tip RT a little further just so that Professor has enough of a gap to fall through into the lower segment. Then walk right, ignoring the Inversion. Eventually you'll turn the level around so you are standing on the sliding ledge on the other side and the Archway is facing north. Keep going so that the Archway is facing east, the sliding ledge is in the bottom, and the Black Menace is in the top right corner. You can walk right up to it and past it; it's actually on a different "plane" to you so it won't kill you; you'll pass behind it. You want to go through the Inversion just beyond the black Menace.
Once you use the Inversion, the Archway will be pointing west. Walk left through the Veil but don't stop; we want to go through the Veil, past the door and then use the other end of the Veil at the opposite side of the Archway. (If that's confusing; walk through the veil, past the door, until the Archway is pointing east and you're about to enter the railed end of the Veil.) Before you enter, tip the level so that the White Menace is in the bottom right corner and the Black Menace is in the bottom left corner, on the button.
Enter the Veil. Rotate right until the Black Menace is basically sitting in the well of a V shape created by the sliding ledge and the western wall of the level. For reference, the Archway should be pointing to the top left corner of the screen.
Exit left and tip with LT so that the Professor is effectively chasing the Black Menace. Once the Archway is pointing south, walk left and use the Inversion. You're now going to walk a long long way left as the Black Professor until you get back to the Veil. Again, you want to walk all the way around the Veil and use the railed side, while the Archway is pointing east. (White Menace should be in the bottom left corner of the screen with the button, trapped by the sliding ledge; Black Menace should be in the section to its right.)
Go into the Veil and rotate with RT so that the Archway is once again pointing to the top left corner of the screen. This time, Black Menace should be held in the V at the very bottom of the screen, in the corner left of the left-side button.
Now walk right out of the Veil, the way you came in, and head to the door. The two Menaces should roll onto or near to the buttons in their sections. Adjust as needed to get them both on the buttons while you are in front of the door.
Here's a full guide to the chapter from Christopher Odd
, all credit to them.
If you finished all of the levels in the Chapter you will unlock the Genius trophy.