I have played through the Verdant Forest twice now, and I believe I have a grasp of what you need to do to be fully successful, particularly with the bosses at the end.
1. Heavy-impact weapon loadout. Killing as many enemies as quickly as possible is essential to progressing far with this activity, so make sure you can kill enemies quickly.
2. Go for precision. Precision kills during the Revelry will spawn up to three Revelry Lights (to differentiate from Orbs of Light) and those go towards your Super. Collect them so you can unleash supers quickly, preferably using ad-clearing supers that can have their sustainability boosted either by killing or through items.
3. Kill ads when fighting the bosses. The ads will provide bonuses to your time limit so you can do more damage to the bosses. I did it my second run through the Verdant Forest, and we came close to killing four bosses.