The Dragon Set contains every equipable piece of gear you can have - from shield and sword to artifact and ring. You may have seen the Dragon ring in a shop once or twice and wondered where the set comes from. It comes from a quest line after Queen of Scales is defeated. To acquire it is difficult but plenty possible and there are many guides on how to do it elsewhere.

The items from the set work together already even if you only have two of them, but the full set does this:
You leave behind a trail of fire that damages enemies.
Your shield bash ignites enemies for a short time.
Your weapon can shoot beams of fire, ignites on hit and does AoE fire damage on the most damaging attack.
Your weapon and artifact cooldowns are reduced.
You do double damage to enemies that are on fire.
You have +50% max health and get full healing after every combat

This of course seems too good to be true.

To acquire the set one must acknowledge that it is the sole purpose of running a game with the dealer, as such one could imagine it best being done in the endless mode, yes?

Wrong. The endless mode includes all the items, including garbage ones, and ones that are good, but you don't need.

What you need is to run a story game, one sufficiently long that you can get the items but easy enough on the starting curses, that you wouldn't lose the gold to buy the items with.

The best bet is the Jack of Scales as the starting curses only affect combat and in a minimal way.

I heavily advise not running any cards that give blessings, such as helpful priest or traveling minsters or heroes return. Not only will blessings take up the encounter rate that you need to cycle through the 32 equipment cards, the latter will replace another encounter with part of itself, meaning it's taking even more of your time. Combat encounters, as far as you can take it, along with high risk card like Royal treasury should give you a chance at it, trading post will also be highly important.

The equipment deck should be only the dragon set and rings. Twisted Canyon, Mr Lionel and trading post all give specific gear if done right (selling your shield prior to Lionel for instance) and will allow you to get what you need that much quicker.

This of course does not guarantee success on the first try or even the tenth - but it's the best chance you have.

Best of Luck and remember - Fortune Favours the Bold