Here is the full list of all 25 Galaxy Admirals achievements.
Accept the invitation and play match 100 times
Send the invitation and play with the invited player 100 times
Win in multiplayer 100 times
Create and play PvP match 100 times
Play with friends 100 times
Send the invitation and play with the invited player 10 times
Accept the invitation and play match 10 times
Win in multiplayer 10 times
Create and play PvP match 10 times
Play with friends 10 times
Accept the invitation and play match 1 time
Send the invitation and play with the invited player 1 time
Create and play PvP match 1 time
Play with friend 1 time
Win in multiplayer 1 time
Teleport and destroy unreachable enemy ship.
Use carrier ship's 'attract' ability to destroy unreachable enemy ship.
Use carrier ship's 'repel' ability to destroy unreachable enemy ship.
Use carrier ship's 'change orbit' ability to destroy unreachable enemy ship.
Use the mirror to redirect the laser beam and destroy enemy ship.
Deliver a total of 10 damage to enemy ships with one shot.
Destroy at least three enemy ships with one shot.
Detonate at least three mines with one shot.
Attach together at least four ships and move them.
Destroy at least three crystals during one round.