TommyJTheGamer did it with 3 decks using cards you get from the start. I was successful with a Druid deck against the first two boss but tried a battlecry heavy Priest deck for the third boss and failed. Tommy's strategy uses more charge minions which is another mechanic that can get over Maexxna's annoying Hero power and I'll probably just netdeck his Warrior deck to try for the clear. If you defeat all boss in Heroic mode (all wings), you'll get a card back.
I'm have not bought any packs other than the ones earn for free and am saving and grinding all my gold for the expansion as I'm on a budget and do not want to spend in this game. The basic card decks are great to try for single casual play too I guess.
Update: I tried the Warrior deck against Heroic Maexxna and still couldn't defeat it. It seems you definitely need Voodoo Doctor early to stall as well as to keep Maexxna's board to creatures with 1 attack or less in order to stand a chance.
Update#2: TommyJTheGamer with the second wing clear.
Update#3: TommyJTheGamer with the third wing clear.
Update#4: TommyJTheGamer with the fourth wing clear.
Update#5: TommyJTheGamer with the last wing clear. This concludes the frustrating (for me) Heroic Mode! I'm still left with the last 5... Note: The Sapphiron Warrior deck contains Naxxramas card due to the difficulty so it is still free-2-play but not entirely basic cards-only.