Beast Within serves as a cheap solution to any problem, while also providing a 3/3 body. This deck also has a land destruction sub theme, between Beast Within, Acidic Slime, and Tectonic Edge. I envision winning many games through this route combined with an early Garruk Wildspeaker or Wurmcoil Engine. Karn Liberated does the job too, and it too is excellent at destroying lands and burying the opponent.
Garruk Wildspeaker provides creatures and doubles as a ramp spell. It's not heavily played these days, but it's quite a good card, and I think it's honestly the perfect card here.
Instead of Primeval Titan, which is necessary with Eldrazi, this deck plays 3 Wurmcoil Engine. This is rather difficult to kill, and it all but destroys anything aggressive.
The real exciting card in the deck is Karn Liberated. This can be cast rather early here, and it wins the game soon after. The 7 walls in this deck both ramp Karn out and protect it from creatures. I can't really say much about what it does once cast, because it just kind of ends of the game. You can destroy some permanents, or start nuking their hand and restart the game. Don't forget you can target yourself and pick the best permanent for after the restart. It also combos well with Contagion Clasp.
The card that ties the deck together is Ancient Stirrings. The biggest reason it's so good in this deck is the colorless high end. It conveniently finds Karn Liberated and Wurmcoil Engine, so the entire top end of the deck is easy to find, ensuring your mana ramp can be put to good use. Ancient Stirrings also finds Tumble Magnet, which buys a lot of time, as does Wall of Tanglecord. Contagion Clasp is good removal in a green deck, and proliferate comes in handy with Tumble Magnet and the planeswalkers. It's a great way to get more value out of Karn and Garruk. Ancient Stirrings also, and probably most often often, will find a land. Tectonic Edge and Mystifying Maze provide ways to gain additional value.
Out of the sideboard, the deck plays Hex Parasite. This is a perfect answer to planewalkers from a non-aggressive monogreen deck. It's an unexpected aggressive creature with a killer ability, and most opponents will be caught with their pants down.
I'm not sold on Corrosive Gale, and don't see a real use for it. Unless you know something I don't, I would recommend changing that slot. Otherwise, the rest of the sideboard is flexible and is full of answers to common problems. Nature's Claim in particular is amazing right now, as it destroys equipment, Pyromancer Ascension, and Splinter Twin.