Here is the full list of all 20 Twin Robots trophies - there are 4 bronze, 6 silver, 9 gold and 1 platinum.
Unlock all other trophies
Finish all the levels
Collect all batteries across all levels
Finish all the levels with both robots alive
Finish all the even levels with both robots alive
Finish all the odd levels with both robots alive
Finish level 22 with both robots alive
Run against a closed door
Die on the spikes over 25 times
Die 5 times inside an acid pool
Both robots die smashed together
Jump 75 times in one level, using the same robot
Share energy when your twin is about to die
Step on all of them in one level
Finish a level using only 1 robot, not switching control even once
Finish level 2 with both robots alive
Press the red button at the last minute, just before your twin gets crushed
Perform 10 consecutive wall jumps
Give all your energy to your twin
Reach the exit with both robots