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