I don't think he was asking how to beat Anti-Monitor, He's asking what strategies could be use with him.

Honestly the map will play a big part when using the Anti-Monitor, regardless of rank. The more open the map is, the more of a target he becomes. Try using the prison map or the JSA museum maps, they're perfect for this. Just hope you win the initiative roll.

BFCs wise, isolation can help protect him from modified combat values. Crosswinds, if unrestricted, would also help even the odds in his favor. Poor Teamwork and Atlantis rising could also be used to reduce the mobility of your opponent's team. High Gravity would also be a bit helpful in dealing with super strength reliant figures, if only a bit. Earthquake can also be used to remove all those bystanders from preventing you from healing later on, maybe even Krakoa(Since AM can keep on attacking anyway regardless of tokens this really won't affect him).

When using him however, be aware of what powers are on the dial. Remember at Rookie level he only has Invulnerability. Also his weakest point is the 7th click where he has no special power, be careful of that click. Attacking is a different matter however. Use Multi-Attack to your advantage. You have 12 range and 2 targets, Psyblast even if for 3 damage TWICE in a turn can beat the stuffing out of most brick figures. His quake with unmodified damage is also a good way to break combat formations up, with the downside being you'll be stuck in a crossfire. Yes he has that wonderful healing power, but it's very dependent on your oqn dice roll. In my trial games with him, i ended up rolling for no healing. That's not something you'd want to end up with either.

Since people would use special objects on him, just know how they work and possibly a way to counter them or use them to your advantage. Shield disruptor will only work if you're in range. It's also a double-edged tactic in that it also affects your opponent's characters within range.

Hope that helps.