The esper who steps up is someone called Won Seonwoo which has a peculiar power combination. He has a sort of precognitive danger sense, which he can use to figure out whether something will go badly, and also a very thorough energy shield which can shield him and anyone inside it from psychic influences as well as from threats unseen—including those in 4D.

"Hello, sir," he says to Cricket.

"You'll do," says Cricket, and he hooks a claw in Won Seonwoo's pant leg and pulls him just a little bit ana so they can start exploring.

That's trippy as hell!! Well, he summons his forcefield, which looks like a hollow transparent sphere of energy centered on Won Seonwoo's x, y, and z coordinates which gets progressively smaller as one gets farther from him along the w coordinate; that is to say, a hollow hypersphere.

They can start exploring.

Cricket sits on people and alerts Woo-young that he is sitting on them and then lands gracefully when they disappear from under or wunder him.

Won Seonwoo is quiet and focused on the task at hand but it seems like the way his shield works is that when something hits it that—hurts? Or something, he flinches every time, especially if he's hit from a direction he can't perceive.

"Are you planning to collapse like a bouquet of flowers sooner or later? You mustn't do that, I could be squashed."

"...huh?"

"Oh, I forgot you are a barbarian. I will talk slower. Do not fall down with backlash! If you fall down, something bad could happen to me!"

He got... a couple of words of that? 

"Min Woo-young-shi, I believe Cricket-shi is attempting to say something," he says into his comm.

Well that's a rude way to put it. "Cricket-san, did you need anything from Won Seonwoo-san?"

"I want to make sure this barbarian does not fall down with backlash! It happened to Haru the other day and if it happens to this guy I could be squashed by one of the monsters. They're a lot bigger than me."

"I'll let him know." Don't laugh don't laugh don't laugh— "Won Seonwoo-shi, Cricket-shi is concerned for your health and asking after your backlash levels."

"—ah. I'm fine to go, still; my backlash is paranoia so once it gets bad enough I'll automatically want to leave, I won't stay past what I can handle."

"He says he's still fine to go, but if you get in any danger there's a button you can press on your commscreen that'll immediately teleport you to me."

"Thank you," Cricket says in Korean to Won Seonwoo with (yes) withering sarcasm, and on they go. He is sitting on a person. He is sitting on another person. Does it help if he specifies where on them he is sitting. This person thinks he's a native monster and is freaking about him sitting on them so he is flapping to be mostly kata of them but he's got a paw on their head.

Specifying where he's touching someone doesn't change much; Woo-young can go off "person Cricket is touching" pretty easily.

Cricket sings to himself a little while he's trotting and flapping and claw-tugging his escort through the dungeon and he sits on SO many people. He's not an esper, he's better because he can do this all day.

Unfortunately Won Seonwoo can't and after a while his composure cracks and he whimpers a, "We need to go. We need to go right now." And once it's cracked it breaks open all the way, and he starts muttering and looking around in barely-controlled panic, ready to bolt. It's a complete change from the placid-if-strained look he'd been slipping into before, and he hates that when this happens he completely loses his ability to return to a semblance of normalcy but he hasn't tried to fight it very much since, as he said, it's a self-correcting problem, as he wants to run away immediately. 

(...it does have some risk of spiralling with him using his power constantly to try to keep everyone out which makes him more paranoid which etc but he's not there yet.)

"Well, don't say I never did anything for you," says Cricket, sighing long-sufferingly, and he leads Won Seonwoo back out of the dungeon. Ana to get through here and there's a little hole that a human can fit through if he tries hard and believes in himself and then they can pop back kata and go down this way and here they are at the portal. They will have a problem if he can't tolerate the pant-leg-clawing approach though.

He flinches and starts to sweat and worry about potential infections if he gets cut but can be led to safety anyway. 

As soon as he's at the portal he turns to Cricket to say "Thank you, Cricket-shi," with a deep bow, before running out through the portal.

Cricket does not understand Korean honorifics, which is good, because he would go around demanding that everyone address him like he was an emperor. (He actually had Ren playing along with calling him Cricket-sama for a good few months before he got tired of it.)

"Is there another one of those lying around?" he asks. "Those people aren't going to sit on themselves."

There is but it seems like they're nearing the end of the list of people whom they know have been kidnapped and are now looking for the core to kill the dungeon.

Then Cricket will look for that instead. He thinks from the layout that it's going to be waaaay in the bottom and all the way kata, wunder a bunch of discarded monster shells (they keep shedding and getting bigger, people have probably noticed the shells falling through the dungeon and if they caught any maybe they'll be useful later). Someone bigger than Cricket is going to need to haul all these shells out of the way.

...Cricket is very useful. Some of these people hadn't worked with him before and he is so useful.

Is there a boss monster? Often dungeons that are this twisty skimp on getting one but...

There is not a boss monster but there are some hermit crab kinda monsters hanging out in the discarded shells.