Edit (02/17/22): This strategy may or may not work exactly as it did in the past on newer versions of the game. I'll share a video link, provided by Ehh Maple in the comments, which is also similar to Dualmilion's guide on the achievement.
10,000 is a lot! so probably best to try for this late game when you're at the level cap. I used a Dark shifted Specter to deal the 10k hit with a Dark Yowie and Light Beetloid for support. Our target is none other than the Specter itself, which you can choose to fight from the Champion Challenge npc in Keeper's Tower.
https://imgur.com/a/8AXDzkqThis was my Specter's skill tree, We're going to use the ability Spectral Cannon lvl2 in conjunction with all the crit dmg+ passives. My Gear was Scythe+5, Cape+5, Impact Ring+5 and Medallion +5. You may be fine swapping some crit dmg for more magic like Moon Sword or Wizard Hat, but I haven't tested that myself.
Edit: Charge stacks are important for boosting your damage enough to breach 10k, try spending a couple turns to build them up on specter before you attack. Yowie is the weakest member here and can be replaced by dark draconov, which has an aura to increase party equipment stats by 15%. This should help make the 10k limit more easily achievable.
For the fight, simply have Yowie use Glorycast lvl3, Beetloid use Enchantment lvl3, and cross your fingers for Spectral Cannon to crit. My final crit was for 10,1xx which is cutting it a bit close, but the setup was sufficient for the achievement.
Troll/Draconoir are other possible candidates as they have high physical and access to the Boulder Toss ultimate. I was able to hit 8,600 using Troll vs Gryphonix without a physical setup so it may be viable.