Royal Jelly Palace is Stratum 4. Stratum 4 is balanced around having 3* gear (as it is right before Tier 3, which requires 4* to enter).

Also, if you're at point blank and facing the target, the Calibur series' charged attack can hit up to three times.

The Royal Jelly has natural regeneration. Poison will briefly disable it.

The Royal Jelly is completely immune to everything when it glows pink and does the spin tantrum. Shock can, if applied before a tantrum, make him flinch during said tantrum and therefore slightly reduce the danger.

Curse puts a serious hurting on him in the first half of the fight (before the tantrums begin).

The Autogun is not such a great weapon.

Sleep can affect the Royal Jelly, but his immunity tantrums are on a timed schedule rather than an attack pattern. He will simply become immune to damage partway into sleeping... and pick up the tantrum where it would have left off if he wakes partway into it.

upgrade your autogun to a pepperbox or higher, it's pretty much a flamethrower which you can use for setting JK aflame to attempt to cancel out the healing with fire damage.

JK doesn't regenerate when pink.

Don't let people discourage you, its not easy but completely doable even with your low gear. First of all you want to have 3 poison/ 3 shock/3 curse and 3 health capsules if you can get all of them(sometimes 3 curses wont drop) after that its all about calibur spin attacks. In phase 1 hit him with a couple spins, then poison him. repeat this until he goes into phase 2(where he is spinning around the room) In this phase he always takes a counter clockwise path, so you can follow in his wake with a calibur charge, wait for him to stop and do his spin, then drop it on him - while your there drop poison/curse shock pot on him too. It takes practice but you can solo him without even being hit more then a couple times by the small jellies, if you have a lot of practice. hope this helps

Hetero

"JK doesn't regenerate when pink."

Yes, but that's not the problem: the brief window of attack will only allow for one charged attack, and he'll have his tantrum back up and ready just before you'd be able to charge up another and get back into range (if you -stay- in range, he'll hit you with his normal attack and delay your charge). As such, he gets maximum regeneration time compared to your damage potential. And that's not even including the part where you might not always have the chance to even hit him between tantrums, if he ended up in an unfavorable position when the tantrum expires (i.e. with an army of minions between you). With other players present, both issues are reduced: four possible charged attacks per opening will definitely overcome his regen, and even if he ends a tantrum in an awkward position, there's a better chance there will be another player there who can reach him.

Also, normal attacks with shield canceling could have worked but he'll break your shield quickly. And then you have to deal with his tantrum without your shield available...

Poison/Curse is key, honestly. I've soloed him once, but that was largely because my party slowly abandoned me on the way down, with the last guy leaving part way through the Royal Palace Runaround. My gear, though, was very similar to yours. The differences being that I had a Swiftstrike Shield, a different gun (Shadow Driver) and a Tempered Calibur, which is the 3* version of your sword. I honestly wasn't sure I could kill him by myself, and I only made the attempt because I hit down at the elevator totally by accident, so I felt I had to at least make the effort or it'd have been a waste of the 10 energy. (I should point out that by the time I soloed him, I'd already killed him in parties a fair few times. I already had my first Sealed Sword and an Antigua by that point.)

Try to keep him poisoned and/or cursed as much as possible. On fire if you can, and possibly shocked if you run out of alternatives. Poison, quite frankly, is key for this fight. Curse is even better. He can't heal while under the effects of either, so if you bring a full stack of both, you can put a stop to that noise for quite a while.

Using the Calibur's charge attack is a perfectly viable way of taking him out, but you might need the 3* one. It's a damned good sword to have anyway, and will work well along with whichever sealed-sword path you eventually take, so don't feel that the upgrade is going to be a waste. The nice thing about the Calibur on this fight is that because the JK is pretty much immune to knockback, the charged swing will hit multiple times, although I'm not sure this holds true for the 2* version.

The nice thing about the JK's tantrum is that he hits the little jellies and knocks them around. He also always spins the same way. Once you get to this phase learn to follow the spin so you can have a charged attack pretty much as soon as he stops. Shield cancel it so you can possibly avoid the regular attack he does right after, and maybe (if you're feeling especially brave) hit him once or twice before you run out to avoid the next tantrum. (Do not try and finish your combo. He will hit you.)

Once you get to the tantrum phase of the fight, btw, is it immensely important that you deal damage at every possible opportunity. His self heal gets about 50% stronger at that point, and if you're out of poison/curse vials, you'll need very drop of damage you can get.

Soloing actually makes JK slightly more easier to defeat, since its HP isn't multiplied by the number of players. You still have to deal with the HP generation and legions of jellies swarming about you, but once you're able to get their tactics down, you'd be able to survive long enough to kill him. I think the main key here is simply being able to cancel out his regeneration. I invested in getting a Vile Striker and its been a very resourceful weapon against it when poison vials are unavailable, being able to poison him while dishing out damage. If you're lucky enough to get Curse vials, all the more easier, as every attack/regeneration attempt does damage instead. Keep him in that state long enough, even if you can't find the opportunity to attack, and you'll be able to whittle away at his health, but never forget to retreat and heal yourself. Its easy to ignore those annoying tiny little jellies, who actually still hit pretty hard when you're not in top gear.

A 2* sword isn't going to cut it against the JK. Upgrade your weapon.

I prefer to solo because the mobs are much more predictable.

In parties I'm not usually dying because of the mobs I'm fighting it's usually because of a tree that was attacking someone else hit me from out of nowhere or someone knocks the mobs into me while I'm dodging.

Solo I can kite, or deal with everything on my own. That's mainly why I solo...Not to mention I tend to afk or get distracted at times so I hate to make people wait on me.