I haven't done the tier-4 version yet, but I've done 1-3. My advice is...

1) Slow monster movement speeds. If you have at least one level of the "Omniclick" talent and at least 1 taskmaster, then use Slisiblyp for her "Slimy" ability. Otherwise, Aegis would also slow all enemies, but he takes far more gold to get that ability.

2) Have a good tank in the front row. Thalia is a great tank. Khouri (any healer) and Dark Gryphon behind him makes him near-invincible.

3) If you're doing tier-4, use splash damage. Nagono will tank your damage for a while, so it helps a lot to be able to kill monsters behind him and clear an area even if he hasn't been killed yet. Buying at least one level of "Lingering Buffs" talent and using any splash card should keep you going for quite a while, depending on your DPS. Slis's clicking with the "Omniclick" talent should be doing that already, but the splash idea is just in case you don't have Slis. Any clicker will work with "Omniclick" for the purposes of keeping the screen cleared of monsters.

4) Probably most importantly, the objective works best when you prioritize boosting monster drops. Billy, Sjin, and Casey are super important here. Ideally, have Mindy mimic Billy and Casey, and make sure to either not buy or turn off Casey's "Carnivore" ability so she gets her "Spice It Up" abilities more often. You want to clear each area as fast as possible. If you have 3 taskmasters, set them all in the "Auto-click" spots to instantly pick up quest drops if you don't want to focus on picking them up yourself.

5) If you're dying by area 2 because the horcrux gets killed, the only thing I can really suggest is to kill something, anything, and then IMMEDIATELY buy Mindy and Billy. Have her mimic him and buy his "Act of Congress" ability right away. Hopefully you'll get enough drops to clear the areas quickly.