1) it has to be effect damage, not battle damage.
2) it has to happen all in one round. So no burning 500lp per round.
There are 3 simple ways to complete this.
1) use Gravekeeper Vassal
2) use Destiny Hero Plasma when Crowler has 4000+LP
3) use Elemental Hero Flame Wingman and destroy an Ancient Gear Beast. This is the one Konami want you to use, since Flame Wingman is also part of the missions
It's not damage in the game mechanic sense. It's either an LP loss (similar to The Immortal of Thunder) or just changing the value to half the current value (similar to Unified Front for ATK). Which of these it is is irrelevant (no card actually checks for either), but it's not damage. (And would say it was if it was.) Whether the mission counts it or not, I don't know, however.
This is the Deck I used and Completed this 2k Effect Damage to Dr. Crowler's Ancient Gear Beast (Unlock Mission): Have to Fusion Summon Wingman and make sure that the Ancient Gear Beast is in Set Mode. Easy!
With SK you change AG Beast into def, Blazeman is for Poly search, Wingeg K is for stall, Goddess for Fusion sub, Ladybug for stall, Enemy controller for stall(or AG Beast to def), Block attack is for AG Beast into def.
Explain to me which one of crowler's monster has 2400 attacks? Knight with equip spell? or with 2 castle? Remember flame wingman inflicts damage based on monster's attack in grave a.k.a. original attack.
I myself used vassal. Buff up her attack and voila! No complains, no whining on the internet.
It worked for me when Vellian crowler buffed his ancient gear beast( Atk 2000 Def 2000) with ancient gear tank. Then I used flame wingman and killed it while having skyscraper on the field. It's easier to when with wingman with skyscraper when ancient gear is buffed, considering it is one of the higher atk monsters he uses has besides AG Golem.