after playing against my friend's joker for about an hour and a half, i have the following to offer:
-joker wants to jump. his grounded options in general are pretty weak and unsafe, and his landing aerials are his best spacing tools on top of having good, consistent setups into grab. anti-air or air-to-air him often enough and he'll have to start going for lower-reward and less safe options like buffered short hop aerials, up smash, etc. just be careful that you don't get too predictable and end up getting grabbed on landing
-once he has arsene, don't respect him too much. going aggressive against him is rewarded since he loses significant chunks of his meter when he gets hit, and his recovery is relatively easy to 2-frame. simultaneously, his aggression becomes better, but he no longer has rebel's guard, still has a pretty exploitable recovery, and loses significant chunks of his meter when getting hit on top of his dramatically increased damage output and kill power. eigaon is strong but can be blocked, traded with, or jumped over. it allows him to cover his recovery a bit better but him overusing it gets really predictable, and if you see it coming you can shield and hit him while he's still in endlag
-go hard for edgeguards, especially when he doesn't have arsene. if you semi-spike him when he's tethering to the ledge i can almost guarantee he's dead by default. even if you don't have a semi-spike, tethers aren't terribly difficult to edgeguard, and if you force him to tether high you can just read it and double jump to cover a higher angle. he's also pretty weak at the ledge even with arsene so if you have basic ledge trapping down you can force him back offstage if you aren't confident in edgeguarding him
-don't bother punishing his smash attacks when he has arsene, i still don't have it in my muscle memory to just respect it lol
-don't get back aired offstage, if you have the resources to contest him or drop incredibly low, go for it
there's likely still a lot i haven't figured out about the mu but that's what i've learned thus far. also i definitely would not recommend trying to outcamp arsene. eigaon is incredibly powerful at counter-camping and he's fast enough that you really can't circlecamp him for 30 seconds