Here is the full list of all 12 Monster Trampoline achievements.
Complete the tutorial
Get a score of 50 or more in a single regular game
Hit a shark in the Pirate Cove level
Hit the UFO with a monster in the Space level
Hit the sling chairs or parasol on the beach in the Oasis level
Hit a chest at the bottom of the sea in the Pirate Cove level
Send a monster flying further than 100m from the arena
Win a game against 3 computer players on regular difficulty
Use a Singularity monster to draw another monster into an explosive
Get 10 or more points from monsters in a single turn
Win a game against 3 computers on Oni mode
Capture a blue monster 3 times in a row for 3 extra turns