Here is the full list of all 36 Star Trek Legends achievements.
Tutorial complete
Complete 10 battles.
Complete 50 battles.
Complete 100 battles.
Complete 250 battles.
Level up your crew 50 times.
Level up your crew 100 times.
Level up your crew 200 times.
Level up your crew 300 times.
Level up your crew 400 times.
Complete 10 skill upgrades.
Complete 25 skill upgrades.
Complete 50 skill upgrades.
Complete 75 skill upgrades.
Complete 100 skill upgrades.
Complete Episode 1
Complete Episode 2
Complete Episode 3
Complete Episode 4
Complete Episode 5
Complete Episode 6
Complete 3 summons.
Complete 10 summons.
Complete 50 summons.
Complete 10 PvP battles.
Complete 50 PvP battles.
Complete 100 PvP battles.
Complete 10 crew rank ups.
Complete 30 crew rank ups.
Complete 50 crew rank ups.
Complete 50 Missions.
Complete 100 Missions.
Collect 30 crew members.
Collect 60 crew members.
Reach Player Level 50
Reach Player Level 99