Might be a little on the exasperating side if it lands on Ick or Slime, though. It's tough enough to beat those levels even with strong combos, and if you got something like Berserker on Slime Pit then you're going to need to pull all the tricks to pull it off (I'm sure it's possible; probably Yendor and scum for APHEELSIK and BYSSEPS)
Really isn't any easy approach to Slime anymore. Every build that used to work nicely has been nerfed pretty harshly. There aren't enough walls on this level to Stone Heart the Goo boss down to size, and the magic resist isn't helpful since the only magic damage monster has the resist-down property. The monsters are all pretty durable so no one but assassins can reliably clean up popcorn (plus you're unlikely to even be able to take out the 8's and 9's so you plateau earlier). If the stars align and you get a clean run Slime Pits might not appear too bad, but the average case is pretty dismal.
Hope for good shops, glyphs, and a good subdungeon.
I beat Slime Pit for the first time the other day (don't know why but I never tried it when I unlocked it) with a Gnome Sorceror, alch. scroll or trisword (can't remember which, probably trisword), and Witchalok (transloc'd in dungeon). That was pretty effective. There are probably better locker choices if you're so inclined.
Currently trying to Orczerker it. Think the trick is to switch from Binlor or Taurog->JJ or something like that, and to remember your magic resists are disposable before the bosses and res-downers are hittable. RBS looks like a great prep choice but I'm starting to think that for Slime Pit it is more trouble than it's worth.
My go-to for beating slime pits is Elf-Wizard-Binlor-Stone Heart. Use to work every time before the Stone Heart nerf, should still work pretty well now though.
Personally I regard Binlor/Stone Heart as an exploit. Certainly the devs didn't intend for Binlor's boons to double as full mana and health restoration if you happen to have this item in your inventory (and if so it's brutally overpowered)