Here is the full list of all 19 Super Exploding Zoo trophies - there are 4 bronze, 6 silver, 8 gold and 1 platinum.
Complete Super Exploding Zoo.
Finish with exactly 2 of each animal in your herd on Dynamite Heights Level 3.
Collect all the stickers!
Survive your own rampage and then defeat opponent on their rampage.
Force a draw in VS mode with only 1 animal left.
Defeat an opponent using Pandas.
Defeat an opponent using Rhinos.
Breed 100 Baby Crocs.
Finish a level with just baby animals alive.
Aliens ate 56 sleeping animals.
Allow the motherships to spawn 40 babies on Dynamite Heights Level 8.
Destroy everything in the Zoo Hub.
Destroy everything in a Dynamite Heights level.
Stay armed for an entire level.
Finish a level with 60 animals for the Hatchery.
Fail a level by deploying a special skill animal as your final animal.
Vandalise all the cars.
Fail by using your last animal to blow up a wall.
Collect your first sticker!