Here is the full list of all 49 Young Justice: Legacy achievements.
Obtain all Trophies
Use all the powers of the heroes
Reach level 40
Buy all enhancements
Complete the game on Hero Difficulty
Unlock all characters
Activate Squad Boost 20 times
Buy half of the enhancements
Avoid search light in Gotham Docks
Don’t activate the Statues in Esagila’s Temple in The Warriors Stage during “Tag Team”
Complete all missions in co-op mode
Don’t be damaged by any trap in Atabey’s Temple Stage during “The Godess Shrine”
Escape the Avalanche Stage during “Go with the Flow” in less than 5 minutes
Don’t break any Statue in the Museum Stage during “A Hostage Crisis”
Complete all challenges
Get all A Grades
Complete half of the challenges
Get 50% A Grades
Complete 1 challenge
Collect all the Alternate Costumes
Get all the Dioramas
Get all Red Arrow Journals
Get half the Dioramas
Reach level 20
Obtain an A rating in all Missions
Finish the game
Defeat Blockbuster
Destroy 350 objects
Defeat Riddler
Collect half of the Alternate Costumes
Defeat Psimon
Complete 10 missions co-op mode
Defeat 500 enemies
Defeat Black Manta
Obtain 50% A Grades
Defeat Bane
Reach level 10
Defeat Icicle Jr and Sportmaster
Complete 5 missions co-op mode
Defeat Killer Frost
Defeat Sportmaster
Answer 5 YJT question correctly in a row
Reach a Score of 5000 in the YJT
Reach a Score of 500 in the YJT
Reach a Score of 1000 in the YJT
Defeat 200 enemies
Complete 1 mission co-op mode
Defeat Cheshire
Defeat the first 15 enemies