Depending on the difficulty and the hero you pick, most of them can be pretty nasty. The heroes that require proper combos are usually less threatening than the heroes that don’t require combos to be effective.
Azmodan A.I will land abilities on you left and right, so you will get nailed quite often by Globes of Annihilation which hurt more and more as the game progresses. A.I Azmodan is very much aware of enemy team positioning and will snipe players that are low on health.
Genji A.I can snipe really good as well, and the higher A.I difficulty will often times use Deflect when you don’t want it to. It is however easy to bait him into using his Swift Strike prematurely (or playing as a beefy hero where the percentage you are at health wise is more than he can doll out) after which point he is a free kill.
Ana A.I can be very, VERY frustrating to deal with. She will almost always land sleep dart on you unless you use a mobility skill or have fancy foot work, will heal any teammates that are low with Eye of Horus (the other heroic is not as annoying), is very accurate with her healing darts, but does not use her grenade appropriately. Still highly annoying.
Li-Ming A.I can be pretty nasty if you do not have a minion wave between you and her when she uses her abilities. I had the misfortune of playing against one that actually took all the arcane orb talents and glass cannon. It was really risky chasing anyone out of lane while she was alive, as it was very likely who ever was doing the chasing would be intercepted by an arcane orb and lose a hefty amount of health.
Kel’Thuzad A.I can be very scary with how often they can get the hero quest done, but they are not smart enough to really stay behind their teammates sometimes. While it is extremely rare for them to land a combo, they can still hit pretty hard.
Sgt. Hammer can be absolutely frustrating to deal with as she will often prioritize you over everything else, and will always use her knock back and thrusters when things go even remotely south. If you are playing as a melee oriented or squishy hero, you are going to have a very rough time with her.
Morales A.I is about as frustrating if not more so than Ana. If she sticks near her team and you lack the ability to AoE damage the entire team or focus her, you will be fighting a near constant team fight that will constantly shove you back. Though she does get stupid and go off on her own or over extend at times.
Valeera A.I will sneak up on you and gut you like a fish if you are not careful. In team fights though she is pretty worthless, but if you over extend by yourself and she is nearby…
Raynor, Valla, Zul’jin, and Greymane are pretty nasty at the higher difficulties. Ranyor and Valla will dismantle you if you are not careful and they pick the right talents. Zul’jin can as well and can be disturbingly accurate with Guillotine (I witnessed him take out a flying Falstad once with it) and if the bot picks the right talents and gets enough kills under his belt he can zone you about as well as Hammer can. Greymane can and will tear you apart if, again, he picks the right talents, but even without going a meta build if you let him he will send you running to the healing well or back to the hall of the storms.
I am sure there are plenty of others, but those are the ones off the top of my head from the assassin and support side.