The "To the ****" achievement appears to be bugged - at least with some sources.
The achievement asks you to do 350 non-combat damage to an opponent, but it doesn't seem to register all sources of non-combat damage. For example the cards "Vito, Thorn of the Dusk Rose", "Sanguine Blood" and "Enduring Tenacity" all deal damage to an opponent equal to the amount of life you gain. These don't seem to trigger the achievement damage.