Here is the full list of all 15 Kick & Fennick trophies - there are 13 bronze, 1 silver and 1 gold.
Earn a diamond star on every level
Complete the game on Hard difficulty
Finish the game on any difficulty
Defeat the robot at the end of chapter 1
Defeat the robot at the end of chapter 2
Knock out the robot at the end of chapter 3
Escape the robot at the end of chapter 4
Wake up from a deep sleep
Find Fennick
Find a way to the Core Tower
Find all special gears
Jump 1500 times
Get saved by Fennick 50 times
Shoot down 200 enemies
Collect all outfits