Wild Card is a set of four story related quests in the Yes Man quest-line. To get this achievement you must complete all four of them.
You get the first three of these quests by talking to Yes Man, a securitron robot who you first meet in Benny's suite during the story quest 'Ring-a-Ding-Ding Baby.' These are those three quests.
Wild Card: Side Bets.
To complete this quest you have to make contact with the five tribes (Brotherhood of Steel, White Glove Society, Omertas, Great Khans, Boomers). From there you can then either ignore them by simply telling Yes Man you want to ignore them, eliminate them as a 'threat' by killing them, or with several you can sign them on to help you out in the upcoming battle.
You'll come accross most of these tribes even if you do other questlines anyway, so even if you don't want to do the Yes Man questline, it's worth just taking to him for this easy quest and xp.
Wild Card: Change in Management
This quest involves getting rid of Mr. House. Again, something all of the questlines, (bar Mr. Houses of course) want you to do. If you already killed Benny and got the Platinum Chip off him then this will be a very easy quest as well. You'll just need to follow the quest marker. If you are on very freindly terms with him, you won't even need to fight the Securitrons (well I didn't have to, not sure if it was a bug though). Just either choose to kill or disable him when prompted.
Wild Card: You and What Army?
This is the hardest of the Wild Card quests, especially if you are hated by Caesars Legion. You have to go to the Bunker located under the Fort, Caesars main base, and fight your way through all of the Protectrons there and then upgrade his Securitrons with a software update, or something to that affect. If you are at least Neutral with Caesars Legion then this will be a whole lot easier as you wont have to slog it out with the Legion before you even get to the bunker.
Finally, you've done those quests Yes Man will give you a final quest.
Wild Card: Finishing Touches
For this, the only thing you HAVE to do is activate the El Dorado Substation. Just east of Black Mountain. Yes Man will however also give you the option of saving President Kimball (this will grab you the 'You'll Know it When it Happens' achievement) and to try and convince the Followers of the Apocalypse to help try and contain any riots and such in the Strip and Freeside. You don't have to do those things to get the achievement. Just head to the Substation. If you're idolised by the NCR then they'll let you in no problem, if not just dress in NCR gear or simply kill them all. There's only 5-6 troopers there, not much of a challenge for a mid-level character. Once you turn it on and report back to Yes Man the achievement pops.