I have tried looking and I do not know if I have just not looked in the right place or not but what skill set/s are being used for the runs. Would like to know so I can go ahead and work on purchasing or leveling them up.

It's been a while since I played the game so I can't tell exactly which ones we usually use for speedrunning. I can guess it's all about the maxed out weapon damage and stamina recovery ones.