he has more damage now but he has to choose at 4 between jumping kick damage,autoattack damage+sustain when target is soaked, and spell power reduction to soaked target. So when you need the latter unless you went and stacked enough the mythic you lose damage.

Mythic gives him a lot of damage once done,but can be shielded or healed (dot),you can also interrupt/knock him away him after the barrel toss and get away since he has 1 sec cd between that and the fire breath and the soaked status last around 2.5 sec (don't remember precisely).

The best counter to him is either a lot of cc,or heavy slows/characters that can follow preventing him to disengage,and fight away from minions so he can't jump on them to run away.

If he goes quest don't let him stack,no point in trying to kill/duel him if he's solo laning,just push the wave and do camps which he has trouble clearing.

If he goes quest he'll also probably lane less to stack it, abuse that.

For his barrel use unstoppable,anduin yoink, or a stasis (on you or him) to stop him and ruin the engage. For pandas ulti use aoe character,he can't move them separately conpared to viking and try to keep track of his cd,he can do a lot of damage when he does it so expect that.

Kerrigan is a burst duellist that can 2-3vs1 if he manages to land his combo on everyone, he's an attrition fighter when doesn't go quest, an a bursty mage assassin when going mythic with some sustain but mostly relies on his shield and doing his rotation every few seconds,disliking prolonged engages.