Before bringing my own suggestion in, I just want to say that this is among the worst "fixes" I can ever recall seeing.
It's a terrible change from CG as it mainly messes up the very mirror they claimed they didn't want to mess up, while doing little to prevent the counter they claimed to want to stop. It does mess with another longstanding counter though and it does result in more time in game, so probably it's a success by CG's measure.
Anyway, my strategy (with a very low sample size so far) is based on playing for true mirror with fury, bomber, dagger starting to leave you less susceptible to P1 and other easy counters.
If you win the coinflip = profit, easy. No further words to that.
If you do NOT win the coinflip my approach is basic with Dagger, heal or mass assist with fury (based on health status, shouldn't matter much), aoe with bomber.
Levi first turn use 2nd special (the usual opening move with Levi). Somewhere around here, the enemy Levi will get 2nd turn and use sabotage the hangars.
Oon Levi 2nd turn, bring in Reaper (do not use sabotage hangars, get Reaper in first). This will NOT allow you to move ahead of enemy Levi, but will pull back their TM so that you are level and every subsequent turn is a coinflip between the cap ships.
Levi next turn, sabotage the hangars. If you go before enemy you should be just before they bring in their first reinforcement and it will die.
Usually at this stage of the battle, nobody have been able to do much real damage to the other fleet (again, this change is so stupid).
Levi next turn, bring in MK6, nuke their bomber (I've seen other suggest to nuke Dagger, this might be a better option, feel free to do your own testing). Enemy will not bring in their 2nd RI just yet, since they used sabotage the hangars on Levi 2nd turn, so they will NOT bring in MK6 to nuke one of your ships.
Now, final turn for Levi have 2 options
1) you go first and are able to ult = profit, easy win.
2) they go first and ult you, and this is going to be a long one.
In my (limited) testing, with their bomber gone you are able to win despite enemy ult. You should still have Fury, Dagger, Bomber and MK6 all on the field, work down their fleet and win.
When their MK6 comes in, CG still haven't addressed the bug where it get stacks based on your capital ship, so it will enter the battle with enough stacks to nuke 2 ships, this can be a pain, however you should be able to set it up so that their MK6 have just above 40 stacks, meaning it will nuke and then die to a single hit. I've so far been able to kill the enemy remaining fleet fast enough that the two nukes from enemy MK6 haven't derailed me, but again, part of the rng here is that they often focus your mk6, dropping 40 stacks and not doing any damage, which help a lot.
I do not believe the above have 100% consistency, however it allow you to keep in the main starting lineup that make you less of a target in fleet arena, so it's a win for me.
I do believe that the best Levi counters currently are Exec with P1 followed by Profundity, but my P1 isn't 7* so I'm not running that in arena and Profundity is horrible on defense now so I'm definitely not running that, hence the above super annoying approach for now.
And just to clarify, CG need to do a 4th fix to Levi, because the current situation is just incredibly stupid.