This is probably going to be a long read. First of all, make sure this slime won't block your exit. Save your game immediately since tbh this part is kinda hard esp if you don't have "Resolution" spell which decreases your lust.
Next, you should probably place the barrel here first just to not repeat the mistake I made
After that, just do the puzzles, and beat the slime at the door they unlock. For the first puzzle, the door is at the bottom left. For the second puzzle, the door is at the middle right.
Next, get the barrel on top of the stone button which should unlock the next room and just finish the puzzle there as well. After finishing that puzzle, you unlock the stone door which has the slime boss.
After finishing the boss, just exit the area and you should be able to talk with the wolf guy and you'll be able to continue the quest already.