Hansel and Gretel are the first boss, a two-headed ouroboros found at the end of stage 1-6 "Amythyst Mines".
To defeat them, you must use the trap in the ground which projects a spike each time you change dream modes. This trap is introduced partway through the level and does not appear in any other level.Slinky Walk
Hansel and Gretel have three attacks. The first attack is where they "walk" across the ground like a Slinky; this is when they are vulnerable to being hit by the spike trap. Press
to twist when the boss's head approaches the trap, and the spike will come out and hit them. It doesn't matter which head you hit.Bouncing Coil
Once you've hit the boss, it will flinch, then curl up and start spinning. Its next attack is to lunge forward and bounce off the opposing wall, then the ceiling, and finally the ground on the opposite side of the room before burrowing into the rock wall. You'll need to jump and twirl over the initial lunge and then dodge the boss after it bounces downward.Falling Rocks
The third attack comes next; the screen will shake and rocks will fall from the ceiling. Use punk Giana's dash move with
to dash out of the way. Once this attack is finished, Hansel and Gretel come back and begin the slinky walk again.
You must hit the boss using the spike three times; on the third hit a bunch of gems come out and the achievement unlocks.
Thanks to the wiki at http://giana-sisters.wikia.com
and QualityIsNice for the YouTube video I've embedded. Video used without permission; skip ahead to 8:40 to view the boss fight.