Eren's first mistake is not listening to Levi's hint when he said that his choice of transforming is not wrong. Instead, he chose to trust all the jerks who were panicking themselves and below Levi in real skills and rank.
If he had faced off against the female titan from the start, Levi would have been there and at the very least that would have bought them enough time for Mikasa to show up after hearing Eren's shout. 3 vs 1 sounds like really good odds.
Even on the second opportunity, he would have had most of the elite team backing him up.
Actually, splitting Eren and Levi up was a really dumb decision. So is leaving Mikasa on the forest border to what, stand around? A fucking noob could have done that.
A smarter commander would have made Mikasa Eren's personal bodyguard. She frigging leaves position to chase after him all the time anyway.