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