This is a short run on Bronze difficulty with a Krogan Vanguard. I'm posting it to show people how easy it is to solo Bronze with this character, so maybe if you're new to soloing MP you can see how to do it.
The Krogan Vanguard makes soloing pretty easy, at least on Bronze. His insane amount of health, shields and melee damage makes him almost indestructible. Your bread and butter power here is Biotic Charge, but not for the damage. Mostly, you will use charge all the time to keep your barriers up.
You don't need a bunch of awesome gear to solo with this guy on Bronze. Take the best shotgun you have and slap a blade attachment on there. You won't be doing a lot of ranged damage. Also, anything that boosts your shields is useful.
Don't be a quadless sissy. Roll Krogan!