Get a flying mount, preferably the UFO from Martian Madness.
Go in a big open area like space, preferably away from your NPCs so they don't get one hit killed.
Poke its head or tail (body does 1 damage, since body has 999,999 defense), and kill any mobs it spawns before returning to it.
Make full use of the open space you have. You don't need an arena. That will just help him. He can't navigate as easily in the air without anything to burrow through so use that to your advantage. You picked melee unfortunately so you need to get up close to hit him, which puts you at risk.
Repeat until dead. It'll be a long battle as it has a lot of HP. I've beaten it solo in Expert Mode (as a ranger) using these methods, sometimes only taking 3-4 hits.
Make sure you have as many buff and healing potions as always, they'll help you survive, do more damage, apply debuffs, etc..
Also make sure your modifiers are in check. Is your Ark Legendary? Are your accessories Menacing (for damage) or Warding (for defense)?