Here's a quick step-by-step instruction on how to get this achievement. Note that this guide assumes you got the "Helping Hat" achievement in the first chapter of the game, and I can't guarantee it will work the same way if you didn't.
Also note that you have to let Bramble get taken away, so you can not get the "Medicinal Majesty", "A Royal Pain in the Rear" and "Cell-ebration!" achievements. Day 1:Talk to everyone, clean up all the spider webs, get the web, get sent back to your cell.
Day 2:-Eat the meat you get from the goblin yourself.
-Use the web on the crank at the top of the spiral staircase to open the door next to it.
-Enter said door, and you'll enter what I'll call "the big room" from now on. Climb up the shelf at the upper-left in the next area, open that door.
-Turn right at the pass, then enter the room to the north and solve the puzzle to get the frog.
-Go back to the big room and go through the lower-left passage.
-Use the frog in this next room to get the fly.
-Go back to the big room, and go through the passage to the right.
-Keep going right until you find a "sword" in stone. Grab it.
-Go down to the Blacksmith (Left cell), give her the "sword", tell her to whack the left goblin, get a key. You'll be forced into your room, sleep.
Day 3:-Feed the meat to the giant rat in the cell to the right after coming out from your room, open the chest, get the chair.
-Enter the room before the cell rooms with the two raised bridges. Lower them if you haven't already, cross the right one, then use the chair on the wood pile here to get a coin.
-Go up to the big room, go right.
-Use the key on the small door in this next area, go in there and get the flour (If you intend to go for some of the other achievements) and the
page of heart.
-Then, in the same area where the door was, go north to meet the traveling merchant.
-Use your coin to buy the cure-all potion from him.
Make a back-up save here if you want the "Medicinal Majesty", "A Royal Pain in the Rear" and "Cell-ebration!" achievements!-Go back down to where Mr. Fancycakes is (Behind a cracked wall to the left, right outside of your room). Give him the cure-all potion, and you'll get him in your inventory.
-Go back to the merchant (right from the big room, then north), and give him Mr. Fancycakes. After a brief cutscene, you'll get the "The Lost Unicorn" achievement as well as the axe.
-Go to the room before the cells rooms, take the left bridge, then use the axe on the giant mushroom to get the
page of... wits? (Didn't actually chek the name of the item, but you'll know it when you see it)
-Go back to your room and sleep.
Day 4:-Bramble gets taken away.
-Give the meat to the old couple, then give them the fly to get a weed-growing potion.
-Go to the big room, use the weed-growing potion on the weeds in the center.
-Go back to your room and sleep.
Day 5:-Eat the meat you get from the goblin yourself, bringing you to full power.
-In your room, to the left of the door, check the porrige tube trice to break off the bottom, then climb up it.
-In this next area, grab the coin in the bucket, and write down the songs played on the gramophone (Or you can read the spoiler later for the solution to that puzzle).
-Go all the way to the big room. you can now climb the weeds in the center.
-After doing so, you'll be in a new room. Grab the coin next to the photos and go back out.
-Go back to the merchant (right from the big room, then north), buy the porridge for your two coins.
-Now go up the shelf at the upper-left of the big room. From here, go into the first door to your right, with the pea sign. In here, solve the gramophone puzzle (
) to put the "princess" to sleep, check her mattresses to get the pea.
-Go back to the previous room, then open the door to the north. Enter it to find a new room with a door to the right. Ignore it for now, and go straight ahead.
-In this area, check the goblin with the crystal shoe and it will plummet down a cliff to your left. Use the remaining weed-growing potion at this spot.
-Now, go back to the previous room and enter the door there.
-In this room, you'll find a rose. You'll need to quickly bring it to the old couble, dipping it in the bird fountains along the way (In this order: 1: Next to the pea door. 2: Left of the big room. 3: In the room leading to the three different cells). Set it in the bird fountain next to the old couple, and leave it there for now.
-Give the old couple the porridge. Then give them the pea, pick up the rose again, and give them that as well. You'll get the bone bomb.
-Go back to the big rat who guarded the chest (to the right when walking back to your room), put the bomb in the chest.
-Go to sleep.
Day 6:-Get the bomb back from the chest.
-Go all the way up to where the goblins dropped the crystal shoe (upper-left from the big room, then all the way north). Pick the shoe up from the vines, then go to the right and give it to the goblin sweeping the floor. She'll give you the broom (Irrelevant now, but still).
-Doing this made all the goblins leave the area, now you can use the bomb in the fireplace to blow it up.
-Enter the new area, watch the cutscene and you'll get the final pag, the
page of bravery, and the achievement should pop.
I hope this worked for you! If it doesn't, tell me what goes wrong and I'll change the guide accordingly (I wrote it from memory right after doing it myself). If you also want some of the other achievements mentioned, I've written guides for those as well.
There might be a way to do this that doesn't require the axe (But I never found one). If so, you can do this in a run where you save Bramble instead of Mr. Fancycakes as well.