Hey gang! Hades and I went through and tried to figure out some of the unlocking logic with a second Live account. Here's what I found... these aren't the *only* way to unlock the ships (there are apparently *many*, for each ship), but it's a system that worked:
F-27 Arrow Scout - Starter
F-27 Arrow Eclipse - 10 Kills in Melee
F-27 Arrow Guardian - 15 Kills in Melee
F-44 Rapier II Blade - Starter
F-44 Rapier II Vanguard - Wave 5 in Meteor Storm
F-44 Rapier II Cavaier- Earn Navigator Achievement
A-17 Broadsword Executioner - Reach Wave 5 in Gauntlet
A-17 Broadsword Warpig - 4 Kills in Ranked Duel
A-17 Broadsword Behemoth - Win Ranked Free-for-All
Darket Dragonfly - Starter
Darket Raptor - 10 Kills in Melee
Darket Stalker - 15 Kills in Melee
Dralthi IX Striker - Starter
Dralthi IX Shank - Wave 5 in Meteor Storm
Dralthi IX Rhino - 1 Kill in Ranked Free-for-All
Paktahn Phantom - Reach Wave 5 in Gauntlet
Paktahn Tusk - Earn Hibernation Achievement
Paktahn Mauler - Destroy a Capital Ship
Oh sorry forgot. All of us unlocked the Rapier Cavalier getting the achievement, I think it was just Chris and I's last ship. Don't worry though I'll probably be on later and I'm sure all of us can help you get it.
Note that I *didn't* get the Cavalier this way with my regular account - I earned 'Navigator' very early and it didn't unlock anything.