Here is the full list of all 9 Kitten Squad trophies - there are 9 bronze. It takes around 3-4 hours to unlock all of the trophies on PlayStation 4.
Rescue at least 100 sheep.
Loot at least 20,000 Kitten Coins.
Rescue whales, dolphins, and sealions from Sealand.
Complete 3 bounty quests.
Rescue Olivia from the imprisonment by Sealand.
Defeat the Sheep Puncher.
Collect and use every base weapon in the game.
Purchase at least one type of every customization.
Complete a story quest.