That mutant is running around in fallout 3
Actually, there are five of them. The one pictured is found in the Capitol Rotunda. Then there are the ones in Tacoma Park, Evergreen Mills, GNR Building Plaza and the one found outside of Jury Street Metro Station.
They are all pretty easy fights if you prepare for them and go about it fairly intelligently.
The one in Tacoma Park you can use the Talon Company artillery on it.
The one in Evergreen Mills can be safely killed from the cliffs above with a decent sniper rifle (it will take a while even with a gauss rifle).
The one in the Rotunda you can cripple with a dart gun after it gets done picking its teeth with the bones of the Talon Company mercs in there with it. Then gun it down from outside of one of the doors. Or if you are good with sneak and have a stealth boy, activate the turrets.
The one at GNR you don't even have to fight, you can just let the BoS kill it. Even if it kills all the other BoS members, Sentinel Lyons will wind up killing it (she really can't be killed at this point in the story line). If you want to take part in the fight, do it from the second floor of the building you came through to get to the plaza.
The Jury Street Metro Behemoth is probably the most difficult fight since it occurs out in the open where there is no cover available. I recommend a Fat Man or Experimental MIRV and a bit of luck. Failing that, if you cripple one of its legs you can kite it.
Whatever you do, you do NOT want to allow one within melee distance. They will turn you into a fine red paste if you do.
I found the Super Mutant Overlords to be more of a problem than the Behemoths. Those Tri-Beam Lasers they carry can carve you up faster than anything else out in the wasteland.
Slightly off topic (well, quite a bit off topic, actually), that Moira Brown wench needs to be introduced to all five Behemoths at once. Go out and get advanced radiation poisoning? Go out and get severely crippled? Go dance with the Mirelurks but don't hurt them? Really? Sweet tap-dancing Super Mutants, my Ex doesn't even treat me that bad.