Hope these tips help.

I've noticed a lot of people having a hard time against Tiamat and that Demon Asura Momotarou guy during their quest. Well I did a quick video to show you how to maneuver around them safely so you don't get completely wrecked. This is coming from a Melee Power Sword user but is still helpful to learn how to maneuver around. Also for the sake of keeping this simple(and not killing them too fast), I'm using my starter sword instead of my +30 Kotetsu. Keep in mind this is solo. If you bring a ton of people, things will get more hectic as the monsters do different things.

https://www.youtube.com/watch?v=xKROZBtx_N4

Always have pots. Don't skimp. You can bring 10 per pot inside. Hotkey it before you go in. HP + SP. Liquor is also helpful.

Tiamat

- Vertical Fireball as flying shooting in a cone shape
- Cracks in ground from Vertical Fireballs explode
- Horizontal Fireballs
- Sprint

Attack when he sprints right after he's finished with his Horizontal Fireballs
Keep distance as needed. Pot when needed.

Asura Momotarou

- Forward Lunging Slash
- Poison Slash
- Flying long range slash
- Clone
- AOE flying slashes from him

Circle around so his attacks don't hit you. Attack him after he uses a slash. Keep distance as needed. Pot as needed. You can kill the clone but I usually ignore attacking it.
Alternate method if you can't do this is to bum rush him and unload everything you have. Revive unload again or back off and try to pot and unload again. Repeat before you run out of lives.

The fights pretty easy to do Tiamat isn't really a threat as long as he is on the ground and at lvl 14+ its possible to 3 shot both of them if you happen to have an Axe or Odachi with decent skills

Here, I just made a video showing how I usually do Tiamat, I figured Momo is so weak you wouldn't really need a strategy for him...but here.

https://www.youtube.com/watch?v=mgBWNGovWXM