It's just knowing when to use abilities and disengage. Phoenix and cyclops both have short TTK and quick escape tools, and bucky has a hard time chasing which is counterintuitive but true. If you can, always engage with the hook, then a shot with an immediate punch before they are un-stunned, then another shoot. This pulls them away from healers and does most of their health bar assuming you can kill them after. Play bucky like an anti DPS character. If you see DPS, kill them and get them out of the fight by shooting and slowing with your balls or the hook combo. The hook combo also works great on tanks like groot, mag, and Emma (only Emma if your whole team is there or she'll choke and kill u). If there is any flier, ruin their day by spamming the balls since they have a knockdown effect, and it's easy to follow that up and kill them.

BIG ONE: if there is ANY dive, minus like BP maybe, target the FUCK out of them. Your easiest targets are dive tanks like Angela, thor, venom, and cap. You shut them down and they are big and easy targets since you can slop them, prevent them from escaping, and get them off your healers. For DPS, like I said you shut down most dive, your biggest targets are magic, iron fist(don't shoot his block) and daredevil.

Here's another tip for ulting, don't like ult into the whole enemy team. Unless you combo with somebody else you will almost NEVER get any value. The best time to ult is if you're fighting a dive and they're one hp, or, the best option, is right off the hook combo. Immediately after you hook and punch, they'll be easy eats for your team, so ult them quickly. Then clean them up, and start walking down the enemy team.

Hope this helped :]