To toss, she needs to hold. She won’t hold. Tinya, in all versions, is quite able to shift fast enough prevent that - if she’s lucky enough to catch in the few moments that Tinya’s fist - or foot, or knee, or whatever - is solid. Unless Dinah’s wearing gloves specifically made to hold Bgztlrs - in which case, the fight goes to her - the best she’s going to do is throw off Tinya’s attempt to hit her.
And, pre-ZH, she’s a better - and more creative - fighter than you’re giving her credit for. She, like most of the Legionnaires of her era would have trained under Karate Kid (I), who managed to turn even Saturn Girl, Dream Girl and Brainiac 5, the least physical Legionnaires, into decent fighters. (I don’t think Tinya was specifically mentioned as training under Val, but the ones who were suggest he talked everyone into it, except maybe the real powerhouses - Ultra Boy, or the Daxamites and Kryptonians.) She’s also displayed the ability to non-fatally disrupt a living being’s brain functions - although I only remember her doing it once (‘I’ve been dying to try this out’), and she never explained how she did.
Post-ZH Apparition isn’t near the skilled fighter that her pre-ZH equivelant was - she spent a not-insignificant portion of the run either dead or pregnant - but she still has fast shifting reflexes to make up for it.
Haven’t seen Waid’s PG enough yet to really be sure, but she’s liable to be at least as good as pre-ZH - and likely less straightforward - if the rest of the Legionnaires are any indication.
Phase, I haven’t read L.E.G.I.O.N. recently enough to make much of a comment on, but she was Phantom Girl, pre-ZH, so she likely had the same skills, unless her amnesia was worse than I know.
Don’t forget Dr Zoom and Bizarro. The Society was taking no chances on a miracle turnaround.