The following are known Action Replay Codes for Professor Layton and the Last Specter on Nintendo DS (NDS).

Game ID: BLFE-f0A46820

Press L+R for Max Picarats
94000130 fffb0000
120faa70 0000270f
d2000000 00000000

Infinite Hint Coins
da000000 020faa74
d7000000 020faa76
d2000000 00000000

Max Hint Coins (Press SELECT)
94000130 fffb0000
120faa76 00000064
d2000000 00000000

PUZZLE CODES:

All Regular Puzzles Available (Press SELECT)
94000130 fffb0000
221000d0 000000aa
c0000000 000000aa
d8000000 020ffe28
d4000000 00000001
d2000000 00000000
Do not overwrite your save with these codes ON Press SELECT before entering the Puzzle Index.

Extra Puzzles Available (Press SELECT)
94000130 fffb0000
221000d0 000000e4
c0000000 000000e4
d8000000 020ffe28
d4000000 00000001
d2000000 00000000
920ffee0 0000b9b8
220ffee1 00000001
d2000000 00000000
Do not overwrite your save with these codes ON Press SELECT before entering the Puzzle Index.