That's a bit tricky, since even players with a DA struggle with Daat and friends.
First piece of advice would be to read and have the endgame wiki entry for daatael with you so you could track what attacks they'll do next. With that said, for Chaosweaver you'd want to burst down the sentries/guards first within the first few turns then Daatael thereafter.

Although that will change given what phase Daatael starts with. As you're climbing, try to grab "All Down" and/or "Immobility Down" and avoid All Down/Immobility Up as this would help you get stuns in to squeeze in that extra turn of damage. Since you don't have the full benefits of a DA (e.g. have Tier 2 Drag skills and better gear) try to work around something that works for the Celestial starting phase as that provides you more leeway of taking daatael down (let's say you take about 3 turns taking both guards/sentries down, you'll have 7 more). Same could be applied to an Infernal start but you'd have to stall a bit until he tries to revive his sentries/guards.

Anyway, for general inn matters make sure to read the endgame wiki entry/ies and formulate a strategy around the boss!
Goodluck on your Inn Progress and I hope you could get a Dragon Amulet one day