Here is the full list of all 41 Samurai Jack: Battle Through Time achievements worth 1,000 gamerscore.
Obtain all in-game weapons.
Defeat an enemy using the environment.
Collect all Collectible Items.
Learn all Skills.
Complete a stage using only the Sword.
Complete a stage using only Samurai Fist.
Complete a stage using only the Hammer.
Complete a stage using only the Spear.
Upgrade all weapons to their maximum levels.
Defeat a Boss using a Throw.
Complete a stage without using a ranged weapon.
Complete a stage using only the Club.
Collect all Items.
Complete Cave Of The Ancient.
Finish a stage with under 10% health.
Complete Aku's Tower.
Complete Prison Ship.
Defeat 1,000 enemies.
Upgrade any weapon to its maximum level.
Complete Snowy Forest.
Complete Ruined City.
Complete Aku City.
Defeat 20 enemies using the bow-and-arrow.
Complete Undead Cemetery.
Complete Boon's Castle.
Repair a weapon.
Complete Aku's Mines.
Have a conversation with a character in the world.
Use a Kiai Attack.
Collect 100,000 gold.
Fulfill all in-game accomplishments.
Complete Aku's Mines on Master of Masters difficulty.
Complete Boon's Castle on Master of Masters difficulty.
Complete Cave Of The Ancient on Master of Masters difficulty.
Complete Undead Cemetery on Master of Masters difficulty.
Complete Aku City on Master of Masters difficulty.
Complete Ruined City on Master of Masters difficulty.
Complete Snowy Forest on Master of Masters difficulty.
Complete Prison Ship on Master of Masters difficulty.
Complete Aku's Tower on Master of Masters difficulty.
Complete all stages on Master of Masters difficulty.