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