Here is the full list of all 32 DreadStar: The Quest for Revenge achievements.
Rescue your father
Explore the unknown and come out alive in brutal difficulty
Explore the unknown and come out alive in hard difficulty
Beat the Betelgeuse sector in brutal difficulty
Beat the Mazinger sector in brutal difficulty
Beat the Mazinger sector in hard difficulty
Beat the Betelgeuse sector in hard difficulty
Beat the Cylon sector in brutal difficulty
Beat the Cylon sector in hard difficulty
Beat the Faraway sector in brutal difficulty
Explore the unknown and come out alive in normal difficulty
Beat the Mazinger sector in normal difficulty
Beat the Betelgeuse sector in normal difficulty
Get to level 10
Beat the Faraway sector in hard difficulty
Beat the Aldebaran sector in normal difficulty
Beat the Cylon sector in normal difficulty
Rescue an enemy
Beat the Faraway sector in normal difficulty
Achieve a MAX combo
Warp out of a level
Collect 20000 gems
Collect all weapons
Collect all armors and shields
Collect all engines
Collect all special items
Get to level 20
Get to level 30
Get to max level (40)
Beat all sectors without getting hit