Here is the full list of all 34 Cat Attack achievements.
Adventure with Meow outside.
Take control of the humans by getting through the cat adventure.
Obtain the cursed ring from battling a mysterious character.
Spend 10,000 GP to uncurse the ring, rather than uncurse it yourself. It's weaker than it would be if you uncursed it!
Spend 5,000 GP and purchase the Ship, allowing access to the other continents/islands.
Save the spoiled princess by climbing Darfus Tower and defeating Captain Argor.
Recruit Dave into your party by giving William the GSB after having rescued Mary. (Or by giving him the 2-Liter of Sprite!)
Recruit William into your party by giving him the GSB without having rescued Mary. (Or giving him Coffee if you have Mary and Dave.)
Repair the broken bridge and find the airship. Now you can travel anywhere in the world!
Recraft the Holy sword into the Mythical Sword with some Cetonian Ore.
Recraft Ceto's Axe into Kabogi's Axe with some Kabogian ore.
Rescue Taylor from the Twirly Towers after defeating/placating AWPerative.
Defeat Xookie, completing the game.
Defeat Leanan Sidhe and make it through the gauntlet of bosses, accessing an overpowered character.
Remove the curse by battling 127 times!
Rescue Sean from another dimension and have him join you.
Read the instructions and choose to begin the game.
Save Max from his curse by defeating him as Captain Bones and have him join you.
Collect gifts from Lon by returning to the house with James and Michael in the party.
Complete DM Brahhn's adventure, resucing Trixie and Tawnie from Link.
Defeat the gophers infesting the yard.
Defeat Lucy and gain access to her southern tunnel.
Not a thief... but you collected every treasure chest in the game!
Visit Dax's House after obtaining the Ship and receive a gift from him.
Save Seth after defeating the Gargoyle.
Save Mary after defeating the Gargoyle.
Rescue Amanda from Zombor and have her join the team.
Recruit Maria by defeating Gaia and rescuing Amanda.
Defeat Ice to See You inside the Stiv Volcano.
Receive the Dark Key after defeating Brahhn in his tower.
Defeat Cal and his two shadows to earn the Defender, a powerful sword that increases defense.
Defeat the Angel of Pollution within Gargoth.
Go out of your way to retrieve the Ruby Amulet from the Pyramids as requested by some random woman.
Talk to everyone in Elbonia's training room.