You should be able to earn these without much trouble, if you find yourself getting stuck on any certain mission you can buy a "pass" from The Stash in the "Utilities" section.
The easiest missions give you one star, the medium give you two, and the harder ones give you three. You'll be given three missions at a time until you run out. Once you run out you'll be asked to prestige in exchange for a medal, say yes and the trophy is yours. Certain gadgets will make certain missions easier, so keep this in mind.
- For the run x amount of distance and rub your head on the roof for x amount of distance in one game, they do not need to be done in one attempt. They can be spread out across that playthrough but not multiple playthroughs. Also, make sure that Barry is at the very top or bottom of the level as it won't count otherwise.
- Also for run x amount of distance and rub your head on the roof for x amount of distance, distance covered in a vehicle doesn't count. You must be on foot for the distance to count.
- For reach x distance without using the machine jetpack, you can equip another jetpack, use a head start, final blast, Air Barrys, Free Ride etc.
- For reach x distance without harming any scientists, use the Nerd Repellant Gadget. This will get rid of all of them so there will be none to harm. Certain jetpacks are harmless too, such as the Bubble Gun jetpack and Rainbow jetpack.
- For reach x distance without collecting any coins, turn all magnets off and avoid vehicles. You can still collect spin tokens.
- For collect x amount of spin tokens, tokens collected after death and in the slot machine also count towards the total.
- For vehicle specific missions, you can use the Free Ride gadget to help you out. If you die, you'll start with a new vehicle but if you restart, you'll restart with the same vehicle. This way, you can specifically work on that mission instead of hoping to obtain the correct vehicle by luck. To clarify, if you get the vehicle you want from Free Ride but you don't complete the mission, restart when you lose the vehicle and you can try again.
- To get a "near miss", you must be really close to the missile or zapper, to the point where once false move would kill you. You can get two near misses from horizontal zappers and if you're having trouble with missiles, just, stay in line with it until it fires. Move above or below it then and then get in as close as possible.
- To high five a scientist, just touch off one when you're regular Barry. You can't get high fives if you're in a vehicle.
- For brush past x amount of flashing red lights, just overlap them. They're near the top of the screen and can be coupled with the rub your head against the roof missions.
- Collecting full sets of coins is easier with magnet gadgets turned on.
- For reach between x and y distance, make sure that you cash in any spin tokens when you die, in case you go any further from the prizes you've won. Also, I recommend deliberately killing yourself just before the x distance so you'll fall into it. Don't use the Insta-Ball or Freeze-O-Matic. Don't pick up a vehicle because you mightn't be able to destroy it and die before you reach the required distance.
- Most missions that require you to interact with something else will generally have an accompanying sound effect and/or visual to let you know that you've done it correctly.
^Tips from FootballPsycho on PS3Trophies.org