R1: Tim, although it's pretty close. Gambit's biggest advantage is his acrobatic prowess, but his fighting style (which relies a lot on rapid movement around the place) is very similar to Nightwing's, so Tim does have the advantage of being more familiar with Gambit's style than Gambit is of him. Tim has the superior training what with Shiva, Bruce, and a few other notable martial artists. I think it's Tim 6.5/10. By no means a stomp, but Tim takes the majority.

Round 2: Tim stomps. Tim, with his bo staff, is the second best fighter in the Bat Family (barring Bats himself), and it allows him to contend with people way above his usual weight class, like Shiva, King Snake, and Nightwing. He is confirmed by WoG to be the best bo staff user in all of DC. Not only that, but he has a ton of experienced fighting other bo staff users, like sparring with Bruce and Dick almost regularly, training with Shiva, and a few others. Tim wins this 8.5/10.

R3: If by "no holds barred", you mean bloodlusted, I could actually see Tim cinching the win here. Gambit's first thought is going to be peppering the area with explosive cards and whatnot, but Tim should be able to dodge that fairly easily (he can casually dodge bullets), and I think he can move fast enough to clear the blast radius. His best bet here is to make some distance, and then just drops tons of shit on Gambit. This can be accomplished in a few ways- using his grappling gun to abscond to a nearby rooftop, or just plain running, ducking and dodging (Tim, although not on Nightwing's level, is no slouch when it comes to acrobatics). Then, he can liberally drop tear gas, electric nonsense, or even use some of the kinetic gunk, Cover Gambit with it, and wait for Gambit to either a.) Give up or b.) Try to detonate it, and lose an arm for his troubles. If it's straight up bloodlust, I think it goes to Tim 6/10. If it's just like, a more serious fight, I don't think Tim can win. In character, Tim uses his gadgets very sparingly, so eventually he either gets clipped by an explosive card, or he goes into a H2H fight and gets fucked because Gambit blows up his armor (which is probs almost enough to OHKO Tim.), an all of his gear, bo staff, etc. If it's just more serious, it's Gambit 8/10