Here is the full list of all 26 Legends of the Universe: StarCore achievements.
Defeated Dran
Find the StarCore
Defeated Drecht
Acquired the Gold Armor Upgrade
Destroyed the Navigation System
Destroyed the Weapons System
Destroyed the Radar System
Acquired the Super Strength Upgrade
Destroyed the Shields System
Acquired the Heavy Rockets Upgrade
Destroyed the Engines System
Acquired the Water Walk Upgrade
Acquired the Charge Upgrade
Defeated the Tank
Acquired the Dash Upgrade
Acquired the Silver Armor Upgrade
Acquired the Strength Upgrade
Acquired the Bomb Upgrade
Acquired the Double Jump Upgrade
Acquired the Rocket Upgrade
Defeated Kuran
Acquired the Run Upgrade
Acquired the Long Shot Upgrade
Acquired the Slide Upgrade
Activate all Teleport Pods
Get 999 Zil