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