Contrary to what the other guide says, this achievement does not count ANY damage done by an attack. As the description states, it must be damage done by a Direct Attack. This is damage that reduces your opponent's Life Points when there are no monsters on their side of the field, or you use a monster than can attack through them. For example, if you use Dark Magician to attack an opponent's Curse of Dragon and deal 500 damage, it will not increase the damage done for this achievement by 500.
To grind this simply, get a large number of monsters that have between 1800 and 2200 attack and fight the tutorial duel as a normal duel using a User Deck. Joey has no Spell or Trap cards, although he does have some annoying monsters that can remove yours from the field. Supplement your monsters with cards like Dark Hole and Raigeki to remove those, and add cards like Rush Recklessly and Black Pendant for more damage.
Also, it's good to note that the achievement counts damage you do, not damage your opponent takes. For example, if your opponent has 1000 Life Points remaining and you attack with Blue-Eyes White Dragon, you'll earn 3000 damage toward this achievement.