You need to make sure that you are triggering Nick’s skill just before the mama boss calls the minions into the fight (literally at the moment she starts coming back up after slamming her foot down). By doing that Nick’s lemmings will hit all the minions as soon as they appear which should take them out and do enough damage to refill his bar instantly, allowing him to do it every time they are called in.
Also, have you got Barbossa’s Stitch disc equipped? If this is powerful enough it can slow the mama boss down so much that she isn’t able to call nearly as many minions in.