He could just use Ensnaring Bridge since there's no need to keep a single card in hand. The idea of the deck is to pull out as many of the permanents he needs on the board and wait for the damage to stack up.
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Another way to win on Turn 2 would be to Cast Vector Asp on turn 1. Then in turn 2, activate Vector Asp's ability, cast Invigorate and Berserk
I'd put some Overruns in there to make sure you get some damage going or kill creatures bigger than yours. Besides that I'd get rid of Sprouting Vines. And if you really want to pump it up you can always play with Exploration.