Here is the full list of all 9 Blast 'em Bunnies trophies - there are 5 bronze, 2 silver and 2 gold.
Purchase all the hearts.
Complete 10 Normal Missions.
Pass Survival: Normal Mode
Last 6 minutes without dying.
Last 2 minutes without your weapon overheating.
Destroy a Blocker's shield then shoot its bomb.
Die from a final hit from each bunny type.
Complete 10 Daily Missions.
Survive 30 Very Hard Mode Waves.