Maybe Haste can be drawn from high-level Evloret?

As for the Black Widow... I've beaten it many a time, but I've always had to run from it twice before it became vulnerable.
I used plenty of Thundara (spells from my strongest mage, and Elem-Atk on Squall) and Water, obtained from Quetzcotl's Mag-RF ability or Mid-Mag RF or something.

It takes a fair drubbing to stamp out that machine, but it's fun for a challenge and for the SeeD rank bonuses.

You miss out on the FMV of Quistis dealing to it with the landing craft's emplaced MG, though.