This achievement is for a side quest that is given to you by Thane, one of the makers located at Tri-Forge. You will spot him as you first arrive, either drinking or striking large pieces of wood with his weapon.
Speaking to him at first will yield only a challenge from the gruff maker. If you are lower than Level 5 (roughly) then I suggest you level up a bit. Your first goal will be to defeat him in combat.
Assuming you are strong enough to face him, he will end the fight after 3/4 of his life bar is gone and speak to you. This will now allow you to take the quests for finding the four bosses Thane wants "taken care of".
These bosses can be quite challenging and I recommend you level up before taking them on. I'll detail each boss below. Please note that I fought all of these creatures on Apocalyptic difficulty.
Gorewood - A large treeish creature that has several mid range attacks and a few devastating up close attacks.
Level Recommendation - Any level above 8 on normal, 10 or higher on Apocalyptic.
Gorewood can be found underneath the Weeping Crag area and is a little tricky to find. In this area you will need to climb the outside walls and proceed inside the dungeon. Once inside you will find a skeleton key to open the door out front. Return there and unlock the door. Proceed onwards and to the bottom of this mini-dungeon and you will come to a lake. Swim down the lake and under the land masses to emerge in a little cove on the opposite side. Once you approach the large area the battle will begin. Dodging is key to surviving this encounter and you want to stay close enough to Gorewood to attack after it does, but you need to watch out for its ranged attacks as you can get snared and Gorewood will inflict some big damage. I summoned fire ghouls to help me fight and the added fire damage was a real helper. Once Gorewood finally falls, you will be rewarded with a unique Maul, the Gorewood Maul (Level 10).
Bheithir - A large, fire covered bird that deals some decent damage but only has a few attacks.
Level Recommendation - Level 13 or higher on any difficulty.
I actually found Bleithir to be the easiest of the 4 creatures. This large bird is located in the Nook dungeon; however the battle is ONLY accessible after you receive Deathgrip (the hookshot). If you have already cleared the dungeon you can take the first right door and follow it. Once you hit the stream of lava in the corner and another door you have arrived. You will actually see Bleithir flying slowly round this large room however the fight won't begin until you Deathgrip across the chasm to the narrow platform out in the lava. Engaging Bleithir isn't too hard, you can mostly rely on Redemption although the fight does tend to drag on following that method. Bleithir will make a grand entrance on one end of the platform, then will spew fire breath out across it. He will then charge at you. To avoid this, you can either time a roll to get behind him (and suffer some fire damage) or you can hang off one of the ledges, and then shimmy behind him and attack. Falling into the lava is a sure way to avoid his attacks, however every time you do you have to wait roughly 30 seconds for the boss to fly around and land again (rather annoying). Once you finally defeat him you will be rewarded with a unique pair of Scythe's, Bleithir's Talons (Level 15).
Achidna - The spider companion of Basileus with some strong lightning and short range attacks.
Level Recommendation - Level 15 or higher on normal, 16 or higher on Apocalyptic.
You will actually encounter Achidna during the main questline so no need to actively seek her out. You encounter her along with Basileus (the third Death Lord the King of Bones wants you to recover). She is located at the end of the Psychameron. Please check out the achievement guide for "The Court of Bones" for more information.
Argul (The Deposed King) - The strongest of the 4, the former King of the Dead, covered in ice and chock full of devastatingly powerful attacks.
Level Recommendation - Level 16 or higher on normal, 17 or higher on Apocalyptic.
This guy is a royal pain but well get into that shortly. He is located in the Lair of the Deposed King in the Kingdom of the Dead. Finding his room is fairly easy as the dungeon is pretty small, when you hit a large elevator that takes you down into an icy lower room, you're right at his front door. As you approach the frozen king he will break out of his ice prison. Be ready as he immediately attacks with a strong stroke of his mace. When he does these heavy attacks his mace gets stuck in the ground for a few seconds, this is your one chance to move in for the attack. Once he gets unstuck however, move to a safe distance and be ready to dodge like mad. If he does hit you with that heavy attack and you survive, you will be frozen and will rapidly need to press B to break free and stop taking cold damage. His attacks are fast and strong so be on the lookout and wait for him to get his weapon stuck. After his life bar drops to half he will add another attack to his repertoire, he will do a fast spin attack which is very hard to dodge. I recommend when he preps this attack to get to the other side of the room and wait for his usual opening. After a tough battle you will eventually kill him and gain a legendary Scepter, The Scepter of the Deposed King (Level 20).
Finally after having bested these 4 creatures, return to Thane and after you individually report that each creature has been disposed of, the achievement will unlock.