The full list of orb locations and how to get them can be found here: http://jakanddaxter.wikia.com/wiki/Jak_II_Precursor_orb_loca...
However, I must HIGHLY recommend not even attempting to get them all legitimately on the Vita version. The framerate issues make the game highly difficult to complete normally, and beating the race times in particular is obscenely difficult due to the framerate drops.
Luckily, there is a glitch that was present in the original PS2 versions of the game that made it into the PS3 and Vita ports that will allow you to get all the orbs you need by doing nearly nothing. First, you will need to start an "Orb Search" side mission where you are tasked with finding a location somewhere in the city marked by an orb. (there are quite a few of these side missions, and the glitch works for any of them). Go to the orb's location, but rather than picking up the orb, jump above it so you are falling in a way that would cause you to land on it, then pause the game. If you restart the side mission in the pause menu at this point, the game will register you as having picked up the orb from the fall, but will restart the mission anyway, and you can use this to get as many orbs as you'd like. Here's a video of the glitch in action:
To give you an idea of how necessary using the glitch is in the Vita version, I actually went through the trouble of getting all the orbs legit, but one of the races glitched on me and only gave me 6 of the 9 orbs for getting the gold medal. So, even having done everything legitimately, I STILL had to use the orb glitch once to get the trophy.