How do you get in close enough to hit him without burning alive?
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Come back later. I first fought Bheithir around level 10 and got my *** handed to me. Came back at level 18, finished her before I hit half health. Use teleport slash to get behind her and hit her tail. She will jump in the air and cause an explosion so be ready to dodge. Just stay behind her so she wont use her fire breath and if she does use teleport slash to get out before you burn alive.
Think I beat her at 12 or 13. Easy way is to use the gun mainly and shoot her until she closes in then walk towards her and teleport dash through her to the tail, attack once and roll away a few times, then walk backwards and shoot till you reach the end and repeat. It can take a little bit but its very safe and easy once you get it down.
"I'm a love machine and I'm ready to plow the fields of exstasy. oh yeah!"-Fable-TLC
I beat him at level 11 on normal. It's a pretty trivial fight if you have the omega blades and use the ranged attack.
Beat her at level 10, can be a bit frustrating if your not used to fighting her in such a small arena.
After a bit of trial and error I found out that you can actually go over the ledges and hang from them. (like how you usually shimmy along walls) Careful though as you can still fall to the lava down below. The trick is to only slightly tilt your analog over the edge, do that and your free from her flamethrower.
As for tips in beating her, use the gun when she's far. Dodge or Teleport slash to her back and wait for her tail to swing, once she swings, attack the tip of the tail. When she takes to the air, get outta the way fast cause her slam hurts.
Also if you got Exhume, it'd help too by distracting her, allowing you to score more hits on her tail. Don't be afraid to stock up on potions and Reaper form.
I fought Bheithir around level 12, when you have access to the Necro skill Murder (the one that summons crows). Make sure you max the skill so it summons all 3 flocks (you can always respec at Vulgrim for dirt cheap).
The fight is actually rather simple, Bheithir is really slow and will take his time trying to get to you. What you do first is cast Murder so you apply a constant DoT (damage over time) on the boss. You then run a safe distance and just shoot him with the pistol while constantly applying Murder (the pistol shots regenerate a lot of Wrath). When Bheithir gets near you just hang on the ledge and kinda creep around him making sure you don't get hit by his swipe. Do this over and over and you'll eventually win without getting hit.