Deleting Save Data in Pirates of the Caribbean: At World's End (Nintendo DS)
There is no in-game "Delete Save" option, and the Nintendo DS system menu does not allow per-game save deletion.
Your Options
Start a New Game: The game will prompt to overwrite the existing save slot. This is the intended way to "reset."
Full System Format (Nuclear Option): System Settings → Format System Memory. Erases ALL saves, settings, DSiWare, and Parental Controls on that DS/DSi/3DS. Back up anything you want to keep first (not possible for retail cart saves without homebrew).
Advanced / Homebrew Only (Requires CFW / Flashcart)
Checkpoint / JKSM / GodMode9 (3DS/DSi): Backup/restore/delete individual save files.
NDS Backup Tool (DS Flashcart): Dump save to SD, delete on cart, restore later.
For 99% of players: just start a new game. The old save will be overwritten.