Here is the full list of all 20 Final Core achievements.
Reach the 10th wave of the arena.
Have the mobility, damage and shield buff active at the same time in the arena.
Upgrade any part to 4th tier.
Level up for the first time and obtain the Core Beam.
Die for the first time in the arena.
Reach maximum core level for the first time.
Become the champion of the arena in the Fighter category.
Become the champion of the arena in the Cruiser category.
Become the champion of the arena in the Dreadnought category.
Become the champion of the arena in the Titan category.
Become the champion of the arena in the Corevis category.
Reach the 50th wave of the arena.
Beat the regular set of arena challengers.
Beat the empowered set of arena challengers.
Beat the grand set of arena challengers.
Beat the ultimate set of arena challengers.
Beat the apex set of arena challengers.
Win a 1v1 skirmish.
Meet all the mini-bosses in the arena.
Quickly defeat multiple waves in the arena.