Here is the full list of all 27 StarCore Legacy achievements.
Unlocked All Teleports
Unlocked All Maps
Got the Rockets Upgrade
Got the Strong Rockets Upgrade
Got the Longshot Upgrade
Got the Slide Upgrade
Got the Run Upgrade
Got the Double Jump Upgrade
Got the Bomb Upgrade
Got the Dash Upgrade
Got the Push Upgrade
Got the Strong Push Upgrade
Got the Chargeshot Upgrade
Got the Water Walk Upgrade
Got the Silver Armor Upgrade
Got the Gold Armor Upgrade
Found the StarCore
Defeated the Tank Boss
Defeated Dran
Defeated Drecht
Defeated Kuran
Defeated the Shields Boss
Defeated the Engines Boss
Defeated the Weapons Boss
Defeated the Radar Boss
Defeated the Navigation Boss
Held the max amount of Zil