Frag mines work best. Get a good collection of at least 20 before entering an area that may contain Super Mutant Overlords.;
, A rifle of any kind will suffice.
 Save before entering.
 Take aim with V.A.T.S. Lock onto the weapon the Overlord is carrying (generally a tri-beam laser rifle).
 Get in two good shots, at least. This will break the gun in the Overlord's hands, rendering them defenseless.
 The Overlord will not flee like regular Mutants, but instead attack with its bare hands.
 Wait for it to plow into it, then perform the same maneuver again.

Stock up on mines.
Bring along a precision gun.
Travel to the area boasting the Super Mutant Overlord.
Locate the Super Mutant Overlord.
Fire.
Bring out your land mines.
Sidestep its punches, then throw out a mine.
Keep laying mines until the Overlord is dead.
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