If Drakuseth attacks a planeswalker and that planeswalker is reduced to 0 loyalty from the damage caused by Drakuseth's ability, Drakuseth continues to attack. It can be blocked, and it won't deal any combat damage if it's not blocked. The same is true if Drakuseth attacks a battle and that battle is reduced to 0 defense from the damage caused by Drakuseth's ability.

You can't choose the same target multiple times to have it be dealt 6, 7, or 10 damage.