kivatt
Kono Dio Da
This is what I meant by using his Freeze breath.Doomsday breathed fire on an old version of MMH. New MMH's relationship to fire is very different even from the psychological weakness the old version had. Like I said, it's basically PTSD (Post-Traumatic Stress Disorder), meaning it's sort of like a phobia. But he's been in several scenarios where he's had to deal with heat/fire/etc. and had no problems recently. For example, when he was flying at high speed back into earth's atmosphere and there was heat/fire all around him due to the friction of re-entry and he just ignored it. The times it has affected him, it's sort of stunned him and then he's been fine moments later.
As for psychic stuff, Superman's mental defenses are not what they used to be, while MMH's telepathy is way more powerful than ever. He's gone up against a bunch of people with mental defenses that they thought would protect them and he's just laughed at them. He's mind-raped so many uber-powerful entities that previous MMH couldn't have (Despero, for example, who he beat in a single page).
Also, how would freeze breath and heat vision beat phasing? MMH phases through energy attacks all the time, and has even done it against Superman.
As for strength, it's pretty up in the air. Superman is obviously stronger than he used to be, but we have yet to see an upper limit to new MMH's strength. He has yet to be physically beaten by anyone, or failed to lift anything. He did face Apollo--a guy that in-universe sources put on par with Superman. Apollo got pissed and tried to punch MMH's teammate. MMH stepped in the way and let Apollo hit him square in the face, and it knocked APOLLO on his ass while MMH just stood there.
Oh and there's this, which is from the old universe, where MMH wasn't as powerful as he is now:
He did this against Ghost Solider who was becoming intangible when he was fighting him.