Radula Rooms are Challenge Rooms that appear from Chapter 2 onwards. They are on hidden paths and look like big snail shells. The Rooms will either be a timed combat challenge, an endurance combat challenge, a mini-game, or a riddle from the Cheshire Cat. There are 16 in total.
Completing them will reward you with a Jar of Red Paint. Acquiring 4 Jars of Red Paint will increase your Health Bar by 1 Rose (and also unlock an achievement).
Videos showing locations and beating the Radula Rooms (includes answers to the Chesire Cat's riddles) in each Chapter:
Chapter 1 - No Radula RoomsChapter 2Chapter 3Chapter 4Chapter 5Credit goes to YT User AmTheBroseph01 for the videos