Here is the full list of all 28 Lovers in a Dangerous Spacetime achievements.
Earn one of each type of ship badge.
Finish a level without crossing paths with your partner.
Defeat King Cepheus.
Escape a white dwarf without shooting or ramming it.
Defeat Orion.
Deliver the final blow to Orion using a solar flare.
Pirouette 15 times in a single level.
Defeat Cetus.
Throw a gem into a station that is being used by another player.
Defeat Ursa Major.
Beat any level in two player mode.
Finish the tutorial.
Use every station in a single level.
Beat any level with the help of your trusty space-pet.
Finish a level after removing all fog of war.
Finish a level without taking damage.
Fill up all gem slots in a fully upgraded ship.
Play through a campaign without using any gems.
Rescue every captured friend.
Defeat Ursa Major without taking a punch.
Defeat Cetus while its head is underwater.
Remove all of King Cepheus's shields.
Have 10 unused gems in your ship at one time.
Use three different types of Yamato weapons in a boss fight.
Survive after being fully enveloped by a bomb trap.
Kill 20 enemies with security guns in a single level.
Have 20 cells at one time on the Metal-Beam shield.
Make two Power-Metal missiles collide.