I assume you have led him close to your spawn point so that when you respawn he attacks immediately.

Run!!! Dodge his ranged attacks and lead him away some distance. It works best if you lead him to a wooded area. Lose him in the woods, then circle back around to your spawn point out of his sight.

Elkthyr will remain close to where he last saw you. You can take your time gathering materials in other locations and crafting the weapons and armor you need to beat him.

Once you have done this, go back to where you left him and kill him. A bow and arrows work pretty well especially if you can craft some fire arrows. You will need feathers, wood, and resin to make them.

I like using the bow because you can attack him while remaining out of range of his melee attacks. If you prefer melee, learn to dodge and craft a shield and a melee weapons. Elkthyr is weak to piercing damage so a flint spear does more damage than a flint axe or a club of the same level.