Let's start with something easy.
>Weapons
I'm afraid these won't do much, sadly. Even lesser characters in Baccano can easily time bullets and shotgun pellets as well as react to all manner of projectiles comparable to what Bucky has, and Claire has not only made them all look like complete asses, but also dodged bullets and such without even trying. One time, he even dodged a sniper round (or something like that) with his back turned, while talking to his soon-to-be lover Chane.
Melee weapons don't mean much either. Chane is a knife wielder who can consistently cut bullets out of the air, and Claire easily outmatched her. Ladd is stated to be able to punch as fast as bullets, and has kicked Graham's flying, ricocheting wrench out of the air while it was coming at him from behind, and Claire evaded his punches with ease, even doing a handstand on Ladd's arm at one point. Graham has caught bullets in midair with his wrench, as well as perfectly dismantled an automobile while juggling it (without it touching the ground until it was fully taken apart), and he couldn't even touch Claire with his wrench, with the latter even doing a handstand on his wrench from a sitting position when he tried hitting him with it. And so on.
Which brings me to my next point:
>Skill
Sorry, I don't think Bucky's combat skill comes anywhere close to Claire's, and I'm actually really disappointed that nobody brought up Claire's raw feats in this area. Beyond the stuff I already mentioned above:
One time, when two people tried to attack him (one from the front, another from behind), Claire used the reflection from the first person's eyes to see the second person coming, and proceeded to effortlessly defeat both of them in a matter of seconds.
Another time before that, Ladd tried fighting him atop a moving train. At one point while evading this man's strikes, he effectively did a backwards Smooth Criminal lean off the edge of the train while it was still going full-speed, then frontflipped over Ladd's head when the latter tried punching him again, from that position. Bear in mind that on top of having fists that are apparently as fast as bullets, Ladd is a trained boxer.
MCU Bucky isn't even close to this guy in terms of raw combat skill, and the only actual advantage he would have in a physical fight is AP, more due to vagueness on Claire's side than anything else.
Speaking of:
>AP
There is a feat of Ladd Russo shaking an entire room with a punch, and also a feat of him punching through a steel prison door. Does anyone have the scans/quotes for these feats? I know someone who can probably calc them.
Claire can one-shot Christopher, who is above Ladd significantly. So these are important.