How to sucessfully complete a Mayhem Mission
I'm not sure why people say you can't run straight for bank solo with an mm, my bot/forcefield did it many times (even in his 20's) and while he wasn't completly set up when the longbow came through the door, he still dispatched of them quite easily.
As far as I can tele, soloing it is pretty much exactly as OP said, go straight for bank door, kill longbow that follow you through soon after, leave a path of death on you're way to the vault, open vault/deal with ambushes (are their a finite amount of ambushes cause I often find myself getting sick of them, popping a purple or two and just telling my bots to get the door and ignored the stupid swat team that has a limitless supply of dudes), get moneys, find a good place to wait for hero and then pwn them.
Pretty much always finish with 5 minutes left, which while cutting it close, isn't as close as the 2 seconds before I had in a group (granted that mayham was really fun).
Actually Solo it works a lot better if you do the side missions FIRST. I also deal with most of the cops, cars and items I pass as I go.
I do that then the bank and I usually end the mission with 15 to 20 minutes left and a new power. Only exception is I don't usually bother to break the prisoner out of jail if I get that side mission until after the bank as they are more trouble than help on missions. Great for blowing up cars though.
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You can't please everyone, so lets concentrate on me.