I tried playing Doomsday in an Open Series event once, and it was not pretty. It was easily the most difficult deck I had piloting in my entire career. Hopefully Dark Petition makes that much easier. The goal is to find and cast Doomsday, and Dark Petition solves all the problems.
With Doomsday, you set up a pile that either wins you the game on the spot or on the next turn, depending on what's going on in the game. With a Sensei's Divining Top on the battlefield or a cantrip in hand with a spare mana, you can draw the top card post-Doomsday and have a big turn.
Sometimes it involves casting Brainstorm, playing Shelldock Isle (finding Emrakul, the Aeons Torn) and using Cloud of Faeries to untap and use it. Shelldock Isle actually casts the spell, so you get a free turn. From there, winning should be easy. The second option involves finding and casting a lethal Tendrils of Agony, although that's typically more complicated.
At first glance, I don't like the sideboard, but it does pretty much cover all your bases. Either they have counterspells that Xantid Swarm bypasses, weird permanents to Abrupt Decay/Echoing Truth, or there's a difficult matchup you want to surprise with Monastery Mentor. Either way, it should get the job done, but I'm left wondering if there isn't something we can do better.
Aside from a sideboard that may or may not be good, this deck looks rock solid and good enough to play.