Step 1: Get to level 70. Check out the useful guides on the achievement for that, but recognize that going from 60-70 is a very long grind.
Step 2: Get an item level of 1600+. This isn't too bad. If you're grinding 60-70 with the Elemental Evil content you can pick up some decent intermediary gear, including an artifact weapon for completing the fourth zone, "Spinward Rise". That'll probably get you to around 1500. Slot enchantments everywhere and don't forget to equip and refine your artifacts, including your artifact weapon. Pretty shortly you'll get to 1600.
Step 3: Queue up. The dungeon is a 5-player one. If everyone's at just over 1600, you will wipe repeatedly, so doing this with random people is never a guarantee, but it can be done. There are enough people with sufficiently high gear now that they're running random groups that work out OK.
Most of the dungeon is fairly normal, although a bit tougher than you're probably used to at that stage. The final boss though is rough. Lostmauth is a dragon and unlike the open world dragons you only get your team of 5 for this one. Avoid the red zones at all cost. If you fall in the lava you will take damage but not instantaneously die. Going into the lava might actually be better than getting hit by his attacks. The worst attacks seem to be dropping chuncks of the ceiling which is a small red circle under your feet. These come down fast, though and can be an instant kill for a lower geared character. Additionally Lostmauth will periodically, at about half life, fly off and raise the lava level on the battlefield. Snuggle in on the center and get ready to dodge when the lava recedes.
Step 4: Once you've finally killed Lostmauth, collect your reward (if you can, you'll need an epic dungeon key) and enjoy your pop. The achievement will still pop even if you can't claim your reward, i.e. if you don't have an epic dungeon key.