Lovers in a Dangerous Spacetime

When you reach rank 4, you unlock the ability to upgrade to two different classes of ships; the Jelly Roller and the Banana Split. In order to unlock both, you must reach rank 5 and use your rank 4 and 5 upgrades on these two ships. To receive a ship badge, you must complete a campaign with each of the three ship classes (gumball, jelly, and banana) and the achievement will unlock.

***The three Gumball class ships (P, M, and B) do not provide ship badges because they start your ship with a multitude of gems.

for this achievement you must fully complete any one campaign (from level 1 through to the boss), using the first three ships. it does not have to be all in one sitting. you can save after a level and choose resume campaign later. after beating the boss, that campaign will show a badge corresponding to the ship you used. i had all 3 badges on one level, but it will unlock having all three across different levels. (confirmed by another player in the comments.)

you will unlock the first extra ship after reaching rank 5, and you can get the second one at rank 6. you will need to rescue 60 & 80 friends to reach these ranks, so I suggest collecting all 10 friends for each level the first time through. there are 40 friends to rescue in each campaign (10 per level), so it's possible to earn this on your first playthrough. all achievements for this game can be earned on the easiest difficulty setting. the three extra ships that are unlocked last do not count toward this achievement.