By late game, when you're around level 90+ you will be hitting these numbers easily, so this achievement should come through normal play.
If you don’t have the achievement by the end of the game the easiest method is to go back to one of the starting regions and attack a low-level enemy. Your Artes will easily do 10,000+ damage to low-level enemies, if your level difference is big enough. Finishing moves will also deal large amounts of damage. You can also equip a “Warrior Emblem” Accessory to boost attack damage by 15%.