I definitely met the requirements for "phantom black". The others are a bit vague ("Outlast a nuke" means winning a battle where the enemy used a nuke at least once?), but the explicitly specified conditions for most of them were met, and none of the colors unlocked.
As for level, I was on level 2, not level 3, and was talking about the missions to unlock 3. I can see how my wording was unclear.
More broadly, I'm a bit unclear on the point of weapons carrying over between battles. You can (presumably) farm them indefinitely, but shouldn't the goal be to preserve your ships by clearing the board quickly rather than switch to individual shots to conserve ammo while the one enemy frigate left after your initial barrage chains shots and destroys both of your carriers? I wonder if a roguelike format, where conserving both ships and ammo is crucial to continuing a run, would fit more neatly.