Use the mini-map! You can’t keep an eye on the whole field at a time unless you take a glance at the map now and then.
Keep moving. There’s a considerable amount of shoot-em-up DNA in Bardbarian, which means staying put is hazardous to your health. Avoiding enemy shots will keep you alive.
Use Brad’s abilities. It’s easy to forget about Brad’s abilities to buff his team, but those buffs can give you the edge you’re looking for to win.
Find a team that works for you and stick with it. Unless you’re willing to grind, loot will be limited. It’s better to focus on developing a smaller number of characters if you want to keep progressing smoothly.
Don’t let the smaller enemies pass by you. It’s easy to get intensely focused on taking out a bigger foe, but death by a thousand papercuts is a very real possibility in Bardbarian. Clean out the weaker foes first wherever possible.