Here is the full list of all 14 Don't Touch this Button! (EU) trophies - there are 2 silver, 11 gold and 1 platinum.
Get all other trophies.
Сomplete the game
Destroy five different minions
Complete the sixty level
Destroy one minion
Complete the forty-five level
Spend two minutes to complete one level
Death by lasers
Death by falling
Complete the thirtieth level
Destroy 25 vases
Complete the fifteenth level
Death by spikes
Complete the first level