Here is the full list of all 9 Kitten Squad achievements.
Rescue 100 sheep.
Equip one of each type of cosmetic item.
Loot 20,000 career gold.
Rescue each type of sea creature.
Defeat the Sheep Puncher.
Rescue Olivia the Orca.
Completed three bounty quests.
Completed a story quest.
Find all the weapons.