confused me for a little bit since you said ultimate. Ultimate is used for shadow lair version :x

A barbarous shield gives you damage and pierce defense. It's a T2 dungeon, as if the extra defense of jelly did matter anyways.

Armor/Helm: Deadly Virulisk/Mad Bomber Suit/Mask (Mix n' Matching is fine, I don't think there's any difference between either the Helmet or Armor, so as long as there's a piece of one and the other you're fine)
Why: Deadly Virulisk's All-Weapon Slime Bonus will come in handy, and Mad Bomber's only downfall could be a slight decrease in Elemental Defense b/c of the absence of status in RJP. The bonuses for Mad Bomber come into play with the Weapons down below.

Trinkets: Anything you want, really (I can't think of any in specific, perhaps types to correspond to your favored weapon)

Weapons: Dark Retribution, Shocking Salt Bomb, Gran Faust, Biohazard, Graviton Charge, Acheron, Sentenza, etc. (Any combination of these, though if you're using Mad Bomber go with some of the bombs. Prime Loadout would be the first 4)
Why: It's simple; DR has amazing damage output against JK himself as well as against everything but the Royal Minis, the SSB (Not Swiftstrike :P) has the power to practically shut down all slimes, and with the Bomb DMG from Mad Bomber and Slime DMG increase from both the bomb itself and Virulisk I wouldn't be surprised to find that it could OHKO or THKO nearly any slime in the Palace. Biohazard allows you not only to set up amazing rooms full of lag-fest explosions to kill all the things, but the Poison makes it a prime weapons against JK. Gran Faust is your powerful sword for cleaning up the rubble left behind from the bombs, and Curse on JK plus Biohazard's Poison means doom, when with DR. Acheron would be for crowd-control, but if you've got bombs I can't see a point really. Sentenza for the little blips of damage, but Biohazard outclasses it with it's charge-tags and Poison.

Shield: iunno something with Piercing resist uhhh maybe Ironmight? :P
I don't really have a great idea for this one :P

Tada!

I'm disappointed that at nine replies, not only has no one suggested Swiftstrike, but some one has mentioned it without suggesting it. Its tank capacity is plenty sufficient tankage for any T2 mission; Swifty protects me well enough when I occasionally derp into a Lumber's swing, and any excess tank power beyond that is mostly wasted, while OTOH lots of ASI is always hugely beneficial. Heck, I intentionally take it into T3 sometimes, and other players do it more than just "sometimes," because that ASI High is wickedly powerful and ends up being good for defense anyway. Shorter animations make us more nimble, you know. If I want to ROFLstomp any T2 mission, Swiftstrike is the ultimate shield by far, but I'll admit that if you've got a really heavy emphasis on swords then the Med Damage might make Barbara's Thorn Shield competitive.

For weapons, I've tried mixing and mismatching from a handful of Shadow, Elemental and Normal weapon lines, including Nightblade, Shadowtech, Antigua, (just Blackhawk path) Fireburst, Iceburst, Voltech, Fiery Vapouriser, Static Capacitor, Pulsar, (Normal and Elemental) Catalyser, (Normal and Shadow) Troika, Calibur, Autogun and Blaster lines, and a couple of Shard Bombs... I've also tried some Pierce weapons for the Silkwings, though only paired with the Biohazard that I remember: Snarble Barb, Spinecone, Magnus, Needle Shot and another Shard Bomb. After all that, what I've settled on... is not what I'd recommend as "ultimate" for some random person. In general, Elemental damage is most useful, with Shadow second. Shock seems to be the most useful status effect, with Fire second.

What I would recommend for that is the Toxicat line and either Fireburst or Shockburst, depending on whether you're really big on PvP: if I'm not confident that my party won't be bleeding Pez all over the place, like if I'm PUGging or helping a newbie get some tokens, I reach for my Blazebrand and Biohazard. That means fighting the boss, and the "Poison bullet" gun is capable of handling the boss just fine, while the sword's DPS only makes things better; I can inflict Poison and Fire, and am not limited by vial "ammo" or the luck of having them drop for me earlier. This pair of weapons is also what I use when I want to loot the first two levels of Sovereign Slime as quickly as practical, when I don't have enough time to use all of my Mist playing properly and just want to spend some energy profitably because it would cap out otherwise.

When I do have time and feel like visiting that stratum properly, I prefer the weapons I find most fun, which right now are my Volt Driver, Fiery Pepperbox, Kamarin and Biohazard, (though I only use two weapon slots) but this is a very subjective matter of taste; for "fun," there's no such thing as "ultimate" to recommend.

Pierce Max, Normal Max, Elemental Max Skolver Set
CTR VH ASI VH Slime VH Combuster
CTR VH ASI VH Slime VH Acheron/Gran Faust
CTR VH ASI VH Construch VH Polaris
CTR VH Slime VH Construct VH Dark Rertribution
Normal Max, Pierce Max, Elemental Max Swiftstrike Buckler
x2 Penta-Heart Pendant
Divine Veil as a costume helm because wolver helmets are fugly

The op did ask for the ultimate RJP loadout.

CTR on a Polaris?
-.-