A resolve is a mechanic that protects enemy spawns from dying when above a certain percentage of HP; a hit that would normally kill an enemy will instead leave it with 1 HP. “Triggering” a resolve means to activate a set of moves after attempting to kill the enemy spawn when above the HP threshold. Most of the time, enemy spawns will use a nasty move or set of moves if their resolve is triggered.
How To Counter Resolves
All methods to counter resolves require two sources of damage in order to function; a main source of damage to remove the resolve, and then a secondary source of damage to kill the enemy spawn.
Reliable Methods
These methods consistently work for all resolve spawns.
FUA/SFUA
Bonus Attack and 
Super Bonus Attack are awakenings that deal follow-up True Damage (i.e. after damage calculation) when matching certain formations of Heal Orbs. These awakenings allow players to disregard damage control and instead hit to kill as the bonus attack will finish off the enemy before it can make its move. Keep in mind that if awoken skills are disabled for the dungeon or the card with the awakening is awoken bound, FUA/SFUA will not work.
Auto-FUA Leader Skill Effect
Auto-FUA Leaders have a leader skill effect that deals follow-up True Damage, similar to a FUA/SFUA. Again, this effect allows players to disregard damage control and instead hit to kill as the follow-up damage will finish off the enemy before it can make its move. However, if leader skills are disabled for the dungeon or the effect is not activated, then the follow-up damage will not occur.
Situational Methods
These methods are unreliable in that they only work in specific situations.
Damage Control
Since resolves only apply when the enemy spawn is above a certain health threshold, simply controlling damage output to hit the enemy below that threshold will make the resolve disappear. This is situational because damage control is dependent on damage output relative to the enemy’s effective health; if a team just does too much damage, then damage control becomes an unreliable method for countering resolves.
Poison Active Skill Effect
An active skill that “poisons” an enemy attaches a “poisoned” status to the enemy spawn. A poisoned enemy will then take damage every turn equal to the ATK of the card that used the poison effect multiplied by a variable factor. Since the damage from poison is accounted for after normal damage calculation, poison can be used to finish off resolve spawns after hitting them down to 1 HP. However, poison is extremely situational due to the prevalence of status shields, which provide immunity against all status-based effects (like poison).
Delay Active Skill Effect
An active skill that “delays” an enemy increases the number of turns that must pass before that enemy spawn makes a move. Ultimately, the resolve is just a protection against powerful teams; the lethality of resolves is based more on the move that comes after hitting an enemy to 1 HP. With a delay, players have the turns needed to hit the enemy twice without fear of reprisal. However, like poison, delays are extremely situational due to the prevalence of status shields.