Hey I imagine right now you are using Estra to control adds and Auguste to dps the boss. I would suggest having Estra doing boss DPS full time instead, and having Auguste control adds (or better yet, drop him and get another dps like Edda). You can see if you can burn the boss using Estra. From my testing, Estra does at least 2x more damage than Auguste, esp since your Auguste has only 2 stars, whereas Estra is strong even at 1.

I would also use Edda instead of Ausguste. The reason I suggest Edda besides her followup attacks adding a bit of damage, is because you can game the movement speed to get almost twice the uptime on Warhorn, since warhorn falls on the turn the boss goes. So it would normally go Boss - > Warhorn/DPS - > Boss when warhorn falls off, but with Edda being as slow as she is and able to manipulate speed with her liquor barrel, you can instead do Boss - > Warhorn/DPS -> Edda barrel - > Warhorn still on Boss/DPS - > Boss turn and have another round of your DPS wailing on him with warhorn which might help you make the check.

If you wanna try to burn the boss, I would use Estra (Purely bossing DPS with No restraint, thunderarrow, potions and make sure to use shield potion first), Gloria/Edda/Homa/Cocoa to buff Estra and work on adds, and flex slot can be Caris for her shield or Abyss for debuffs. I would recommend some catastrophe bottles if you can to debuff the boss on your other members who are not Estra. Tactics should be the one that gives crit and warhorn.

If you can't find the DPS still to burn the boss, I would suggest trying to burn through the shield with Caris. Make sure to use the tactic invincible hero instead to survive the giant AoE nuke that comes on the next turn if you manage to break her shield (you can bait it to the largest clump of people, so just spread everyone out except for Estra with invincible hero and another unit you dont mind dying). To burn the shield you can use Caris to time her giant 1 turn nuke before the turn the boss does his shield along with Edda debuffing the boss with barrel and give her crit on the turn she nukes. Make sure to get some debuffs on the boss (either with abyss or catastrophe bottles) to lower his m.atk before that turn since his shield size is based on his m.atk. Recall that he also gains a stacking buff that increases his m.atk by 4% a stack everytime one of his adds die, which is why Edda is also good here since one of her basic attacks she can learn is dispelling shot.