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