There is no Action Replay code to access the Debug Dungeon in Pokémon Mystery Dungeon: Explorers of Time/Darkness/Sky.
Debug builds (NDS dev carts, IS-NITRO-DEBUGGER) contain the full debug menu. Retail carts cannot access it without hardware exploits (e.g., nds-bootstrap + Twilight Menu++ on 3DS/DSi with debug ROM). This is advanced homebrew territory.
Enjoy the intended post-game—it's massive and rewarding without debug access.