For this you need Overdrive Ostrich's weapon, the Sonic Slicer. Usually I go for Wire Sponge first when I start X2, so this achievement might be best saved for the Boss Select part of the Final Fortress.
Equip the Sonic Slicer when facing W. Sponge and just pelt him with it - it kills his "weeds" in one hit and it can stop his "Shield" with one strike and allow you to hit him with more shots. When he dies, he'll be cut in half in a short animation before he starts exploding.
Note: this can be done in the Boss Select area of the X-Hunter Base, but NOT in X Challenge mode!