Here is the full list of all 10 For The Warp achievements.
Defeat the first boss!
Defeat the boss in Xintho system
Beat the boss in Achlys system
Unlock the Aylon Cruiser
Win the game in regular mode
Win a game in Hardcore Mode
Reach Tempestra system
Win the game in Hardcore mode with the Standard Frigate
Win the game with a secret ship
Win the game in Hardcore mode with the Missile Cruiser