Whoa, most posters have this backwards. Saying Kakuzu solos, Hidan is useless.. smh. Kakuzu can't even cause any lasting harm to Tsunade, she can instantly heal any damage he manages to inflict. She also has the strength to smash all of his hearts with mere taijutsu. Kakuzu better run.
The immortals only hope is for Hidan to secure a drop of Tsunade's blood- no easy feat if Tsunade has knowledge of Hidan and realizes that's Hidan/Kakuzu's only hope.
Tsunade summons Katsuyu on top of Hidan, neutralizing him, then walks through Kakuzu's ninjutsu assault unscathed as she rapidly restores any wounds she suffers. Kakuzu desperately hardens his body... to no avail as Tsunade relentlessly hammers Kakuzu with a blow to the chest, launching him into the ground where he becomes lodged in the debris caused by the impact. She casually approaches Kakuzu's limp battered form, confident that he's no longer a threat. Kakuzu belatedly attempts to turn loose his stolen hearts in order to rely on the strength of the ninja who's hearts he stole, but Tsunade quickly launches a rain of blows shattering the masks containing the shinobi's hearts, killing Kakuzu in moments.
A segment of Katsuyu makes contact with Tsunade and informs her that Hidan's scythe has been procured by her (as in, absorbed inside Katsuyu), while Hidan is captured within a larger segment of Katsuyu.
Lady hokage accomplishes what none before her were capable of, she captures an akatsuki alive for interrogation purposes back home in the leaf village. :')
Oh, and don't bother saying Kakuzu's threads will save him. Tsunade grabs the threads and swings Kakuzu around like a lasso, bashing him against whatever she pleases.