How and where is the deep place on the map?

Defeat Cipher Head Evice and defeat the trainers with the Shadow Quilava and Bayleef at Snagem Hideout. Sometime after, Snagem Head Gonzap will appear in the boardroom in the hideout and challenge you to battle. Defeat him and he will flee, but not before dropping the D-Disk. Go to The Under and use the disk to set systems for downward travel and the pod will transport you to a corrdor, at the end of which is the Deep Colosseum lobby.

When you clear the coliseum the first time around, the finalist competitor will be Miror B.; after that Nett will send an email about his suspicions of a Deep King. Battle in the coliseum three more times — the two finalist competitors after Miror B. will be Cipher Head Venus and Cipher Head Ein — and you will eventually come across the Deep King. He happens to have a level 45 Shadow Shuckle.

Moneypenny: On the ground in the corridor leading to the Deep Colosseum foyer you will find the Steel Teeth. Give these to the man on the side of the crevice in the Under opposite the disc terminal and he should reward you with the L-Disk. Use this to set the systems for leftward travel and obtain the Amulet Coin.