Don't use any kind of opacity with hair. This is a "fake" and most probably it will only make rendering slower.
Instead, you should probably allow more passes to be rendered (=better AA), so you can just try lowering GIvsAA balance in the Performance tab of Render settings. The default value is 16, so you can check with 8 and 4, but probably not less than that.
Another idea is making the hair a bit thicker at the end, instead of going down to 0 thickness.