Here is the full list of all 33 Sunrider 4: The Captain's Return achievements.
Get 10 hearts with Asaga then pick her at the end.
Get 10 hearts with Cosette and pick her at the end.
Get 10 hearts with Lynn and pick her at the end.
Complete chapter 10.
Get 10 hearts with Sola and pick her at the end.
Fully upgrade the Dominator.
Complete chapter 9.
Cast Divine Prayer 5 times in a single battle without saving and loading.
Simultaneously destroy 5 enemies with Asaga’s Awakening splash damage.
Complete chapter 8.
Complete chapter 7.
End the Crow Harbor battle before time runs out.
Fully upgrade the Arch Angel.
Restore Sola’s lost memories.
Complete chapter 6.
Save the space whales.
Complete chapter 5.
Chain 5 or more melee combos with Icari.
Complete chapter 4.
Complete chapter 3.
Complete chapter 2.
Complete chapter 1.
See the secret end.
Get 10 hearts with Ava then pick her at the end.
Get 10 hearts with Claude and pick her at the end.
Get 10 hearts with either Icari or Kryska and pick either at the end.
Fully upgrade the High Roller
Fully upgrade the Maray
Fully upgrade the Paladin.
Fully upgrade the Phoenix
Fully upgrade the Spell Caster.
Destroy 5 or more enemies at once with the Flier Drones.
Simultaneously hit 5 or more enemies with Sola.