I saw a post somewhere that you can already finish some of the achievements for Darkmoon Faire, even it´s not launched yet and you don´t have specific Legendaries or cards. I can confirm you can manage to complete some of them, if you meet the requirements, but I believe you can only complete them in Ranked mode.
For example, I´ve "accidentally" completed Paladin´s "Lothraxion´s Ballon Shop" just by playing Steward of Darkshire and summoning some dudes with HP or Muster for Battle, Lost in the Jungle... you get the idea. Or you can try it reversed, summon Dudes and use Coghammer or Purifier's Maul on them, I think it should work either way.
Others mention easy completion of Hunter´s "Ride together, Die together" by simply triggering Toxic Reinforcements, or copying the second deathrattle minion on board.
I´m sure there are more, I didn´t have much time to check them out, but if you found out some others, that can be completed now, please share them, so we can gain some sweet XP :)
EDIT: We´ve found another one: Shaman´s "Two Punch Man" is doable with Doomhammer and 2x Rockbiter Weapons, or with any super huge DH attack.
Another to achieve: You can complete the two neutral achievements "Yogg take the wheel" and "Wheel of Misfortune" by playing Casual Duels with mage when you are offered a loot with the new Yogg and manage to play him (The second one needs to be done 3 times with three different outcomes, but it´s not that hard to pull off).