So Akali...

Akali's laning phase is one of the weakest in the game, it looks like she just snowballed off someone not as skilled as her. Plenty of champions can do that much damage that quickly when they're many items ahead. The counter play to akali is the abuse her weak laning phase and win by attrition if you can't 1v1 her.

Yeah, you gotta wreck akali in the lane phase. Counter her with a strong laner like lux, ziggs, or xerath. (AP chogath, while semi-viable will render akali completely unable to CS and will continue to crap on her through the entire game) The other option is to bring someone else who has a shit early game like anivia or vel since even they can crap on akali and scale into mid/late game just as hard. As soon as she finishes the hextech (standard first item for 99% of akalis) she is on a HUGE spike and you should just call for a gank (this is also when 99% of akalis get overconfident) and do not try to engage her unless you are at a large advantage. If you are not the one laning against akali, pray to god your mid isnt retarded and knows how to MIA.

If akali snowballs, the only real option is to stay well grouped and try to force her into a teamfight. This is another downfall for akali and really any mid assassin; when it's 5v5 the team with the ranged mid generally has an advantage since they can deal damage without going in face first where they become an easy target. At the same time keep the area you are fighting in well warded so she can't sneak around the back.

Pink wards early game, gank the shit out of her. ANY crowd control before six will double or triple your chances of getting an early kill. And mark MIA on her every time she disappears, even for a second. If she can roam and get started, it'll be harder to stop her. Here, though, she has a full build, and I hate to say it but there are a lot of other midlaners that would be just as unstoppable with a maxed kit, though it may take them a little more time.

Also, pick Diana into her, if you can. Same power spiking for time, in a similar package with more power. A Diana with pink wards is a terrifying thing for an Akali player, and this remains true after level six.

That's a six item Akali. Either she was horribly fed, or everyone was 6 items and you as Karthus can do unspeakable things to the entire opposing team. She just happens to have gotten her kill conditions off on you. It's not like Karthus is known for his amazing peel against assassins. The 0.29 seconds is a bug from death recap. With the items she had, MotA can't do 900+ damage. You'd need a double proc and that takes more than 4 seconds.

Oracle's Sweeper is a pretty great way of shutting her down and people seem to forget it exists.

I dare say, even if you were expecting to get jumped on, I don't think the average person could react within .29 seconds to even hit Zhonyas. I could be wrong.

any amounts of magic resist and health helps a lot against akali, if you don't die, she doesn't get her R charges refreshed and usually ends up being the one dying

Play Morgana mid. You drop a pool in her shroud bind her when she jumps to you and when you have your R on her you can see her through her shroud. Not to mention Morg can just keep the wave constantly pushed to keep Akali under turret and not roaming, and she can do it from a safe location so Akali doesn't really get kills to snowball, and if she tried to roam just ping it and then take her turret to punish her.

Overall if you know how to play Morg mid she is very strong against Akali, frankly very strong against a lot of mid lanes if you know the match-ups.