Here is the full list of all 42 Jamestown achievements.
Defeat the Dread Sentry.
Defeat the Lady of the Lake.
Locate the Lost Colony of Roanoke.
Complete any level on Legendary difficulty.
Complete any level on Difficult difficulty.
Purchase an item from the Shoppe.
Complete a solo game.
Complete any level on Normal difficulty.
Defeat the Traitor Prince.
Defeat the Last Express.
Defeat the Conquistador.
Pacify the Heart of Mars.
Watch the credits.
Purchase all items from the Shoppe.
Complete a team game with 2 players.
Complete a team game with 3 players.
Complete a team game with 4 players.
Complete a team game with 4 players all piloting different ships.
Complete the Gauntlet on any difficulty.
Complete the Gauntlet on all difficulties.
Complete the Gauntlet without using Vaunt on any difficulty.
Complete any level without using Vaunt.
Sustain a vaunt combo for 25 seconds on Normal.
Sustain a vaunt combo for 45 seconds on Difficult.
Sustain a vaunt combo for 60 seconds on Legendary.
Sustain a vaunt combo for 75 seconds on Divine.
Complete a challenge level.
Complete 5 challenge levels.
Complete 15 challenge levels.
Complete all challenge levels.
Sustain a vaunt combo for 90 seconds on Judgement.
Read through all the story text in the game.
Complete any level on Divine difficulty.
Complete any level on Judgement difficulty.
Complete the Gauntlet on Divine difficulty.
Complete the Gauntlet on Judgement difficulty.
Complete the Gauntlet without continuing.
Complete the Gauntlet on Judgement difficulty without continuing.
Complete the Gauntlet on Judgement difficulty without being hit or continuing.
Complete the Gauntlet on Divine difficulty without continuing.
Complete the Gauntlet on Divine difficulty without being hit or continuing.
Complete any mission playing as the Red Charge ship.