APE OUT

After beating album 4, you will unlock a new level. Press the arrow that appears at the bottom of the screen, in the level select menu, and choose "Break In".

This level has no checkpoints. You have to go in, get the baby and then get back out.
The achievement pops after you run back into the jungle

Based on my findings on the steam forums, bananas spawn both in normal and hard mode, just on the B sides of an album and only if you had a deathless run beforehand, spawning just on the main path - so the path you took during that playthrough.

(In "Break In", they will spawn just after you rescue the baby)

After you get all of them, there will be a minigame with a guy trying to steal all of them. Simply throw barrels at him (you have an infinite amount) and when the minigame ends, the achievement pops. If he succeeds, you will have to get all 10 of them again