Here is the full list of all 14 Pipe Push Paradise trophies - there are 2 bronze, 1 silver, 10 gold and 1 platinum.
Collect all trophies to unlock the platinum trophy.
Clear the first area
Clear the second area
Clear the third area
Clear the fourth area
Clear the fifth area
Clear the sixth area
Repair the easy levels
Repair the medium levels
Repair the expert levels
Repair the hard levels
Finish the game
Secret