Items: Cookie, Potted Plant
You should remember where the Nanometer Shrine area is. It's where you got your training. Now you're returning a full-fledged adventurer. When you enter, you'll find that the layout hasn't changed a bit. You can still destroy the stone columns on the raised areas to the left and right of the entrance. Do so for some coins, then proceed through the door into the next area.
In the next area, destroy the pots on raised ledges and used a charged drill attack to destroy the boulders and continue through the archway, as you did the last time you were here. The next room still contains spiders and plenty of pots to break, as well as the destructible stone pillars and weak walls on either side. Destroy everything as you did before, while making sure to venture into the side rooms for a COOKIE in the treasure chest to the left and the chance to pull a lever in the right room (necessary in order to proceed). Watch out for the cannons and energy beams. Use your Guard Dash to avoid the hazards. Then push through to the next portion of the dungeon, where you'll find a place to recharge your drill if necessary. Beyond use a charged attack to take out the guy standing on the narrow path between the fences and get some junk. Again, break down the fences to have a chance at the stone pillars, and don't miss any of the vases you can smash. Drill the weak wall to proceed.
Through the ruined wall that the Phantom was guarding, you'll find another armored Phantom and an alarm will sound as the screen flashes red. Take him out with your charged attack and a few follow-up strikes to get some Junk, destroy the stone column, then exit through the door leading right. You're on a raised ledge over a room that drops lower to your left. There're also some pots and a stone pillar you can destroy, plus a pedestal. Stand on the pedestal and restore your HP if you need to, then climb down the ladder as you proceed through the room. Take out the spiders that attack (there are three or four), then push the stack of crates against the far wall. Destroy the wooden bottom one and hop on the iron one and from there to the ledge above. Break the vases, then pass through the doorway into the next room.
You should remember this room from before. A staircase is to your left and a hallway pushes past that. Head down the hallway and there are now two Phantoms guarding it. Take them out with a charge attack and some follow-up slashes (though they don't leave Junk behind), then move past where they were standing and left to pull a switch that raises a ledge to the top of that short staircase. There are also a few stone columns you can break apart here if you wish. Backtrack to the ledge you made available, then destroy the nearby pots before you ride it across a fence. From there, climb the platforms while being aware that spiders will drop to attack you. They're easy to beat, of course.
At the top, jump up to the left area and break open some vases, as well as a weak wall with a hole near its base that lets you catch a glimpse of some grating. You'll have full access to a locked door when the rubble falls away, and you'll be back to pass through it in a moment. First drop down to the ledge where the second and third spider attacked and now drop down to pull the lever. This will cause the door above to open and some cube monsters will parade through. Take them all out with your Drill Tornado attack and then climb up and pass through the door.
The hallway you're now standing in heads past some enemies hovering in the air, where you first learned about target attacks. Put that skill to use again if you like, and past those enemies you should break open the various pots before climb a ledge and passing through a door to the right (while using a charged attack to take out the enemy that guards it for some Junk).
Beyond that adversary is the dungeon's treasure room. Break apart the stone columns for some more coins if you wish, then grab the treasure: a POTTED PLANT item. Now you've completed the dungeon for real! Head back to Tiese and spend some of your money on the GAS MASK. You should have plenty of money, since it only costs 980 pockles. You should also have enough Junk to give your newly-purchased mask an upgrade. Do so, then go ahead and equip it instead of your goggles and return to the world of the monsters so you can move on to the next dungeon. Your next stop is Meter Corridor, in Potato Ruins.