Firstly, you must reach Damis. When you climb down the ladder, head East as far as you can, then North as far as you can. Head East and go South as far as possible at the first option. Go East again. You will see a little cave to your South as you go past, if you run into this you can recharge hitpoints and run energy without using vital supplies. After this, take the next turn North, then go East, and you're in Damis' cave. Run around for a while and he'll appear.
There are several tried and tested methods for fighting Damis, and a few will be listed here. See which one looks best for you and try it.
Combat: Magic (also melee or range, but not recommended)
Inventory: A one click teleport, 10-20 prayer potions, and with the rest of your inventory full of sharks or better food. Optional: A couple of super energy potions to be used for shortening the journey through the maze.
Tactic: This is basically making Damis into a regular fight, just a bit harder. If you have ever fought another creature that only uses melee with prayer, this is basically the same only you will be using more potions. Use earth wave/blast and drop him fast. It is possible to use melee or range, but he is weak to earth spells and incredibly strong against melee, so it is not recommended, especially if your melee weapon is something innacurate like a two-handed sword or a halberd.
Inventory: A dragon dagger (poison necessary), a one click teleport, a few prayer potions, and the rest of your inventory full of sharks or better food. Optional: A couple of super energy potions to be used for shortening the journey through the maze.
Tactic: As soon as you see Damis, put on prayer and use all of your dragon dagger special attacks on him. This will lower his health and poison him, but it's the poison we're interested in. As soon as you have done this, run into the safe room to the north west. Hide in there until you can see that his poison damage is as low as 2, and hit him with another 4 specials. Repeat until he is dead.
Inventory: Runes (nature, earth, water, blood/death, and air), a one click teleport, and the rest of the space divided between prayer potions and sharks. Optional: A couple of super energy potions to be used for shortening the journey through the maze.
Tactic: Cast snare/entangle on Damis when you see him, and start using earth spells on him. If you know about Magic PKing, this will be no problem, however for those who do not it can be very problematic indeed. This is not recommended unless:
(A) You are good at Magic PKing
(B) You are able to stay calm over a short period of time (you may think this is not important, but if an Ahrim's hood hangs in the balance you won't be the calmest of people. If you panic you will most likely fail)
It is annoying because the perfect spell for this fight (any ice spell) is unlocked after this quest.