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