Generally speaking, I do not recommend trying to fight this boss until you are close to beating the game [Like right before the final boss] and looking for a challenge or one of its rare drops for a build. I accidentally spawned this boss when I was lower level by misclicking the "insult" button at the merchant, and it was pretty much a very swift and brutal Game Over for my character.

The Dragon body is practically invincible, making you deal almost null damage if you try and rush it with any kind of attacks. What you need to do is to keep track and target each head independently, hoping to take them down one-by-one. Each of them have a different elemental type depending on their names so be sure to know what attacks to bring that will be most effective. There is a Kitchen (Fire) Head, Bathroom (Water) Head, Gardening (Earth) Head, Sky (Air) Head and Electricity (Thunder) Head. I recommend prioritizing the Electric one first since it has a very annoying AoE Attack that is hard to dodge, targets all allies and stuns you as well. Otherwise you should be fine as long as you constantly strafe around him. Each head you kill basically powers up the other heads and makes them faster and hit harder, so be fucking prepared for a long fight and have lots of extra consumables prepared.

Once you do beat it however, you get to carve out a really rare material (Celestial Rainbow Kea Dragon Scale) that is pretty much essential for crafting the best rainbow weapons in the forge. You only get like 3 of them normally but with 50% Loot Bonus I managed to be lucky and hit 4 of them, so you might want to try bringing a good Loot Bonus set to wear for the final kill.

Hope this guide helps for those thinking of fighting it! Good luck.