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

Game ID: C3JE-72C0A1A1

Press L+R to Solve Puzzle
94000130 fcff0000
520f7a44 00000010
12103870 00000100
d2000000 00000000
codes courtesy of gbatemp

Max Pacarats (Press SELECT)
94000130 fffb0000
120fe724 0000270f
d2000000 00000000
Press SELECT to Activate.

Infinite Hint Coins
da000000 020fe728
d7000000 020fe72a
d2000000 00000000

300/300 Hint Coins (Press SELECT)
94000130 fffb0000
120fe728 0000012c
120fe72a 0000012c
d2000000 00000000
Press SELECT to Activate

UNLOCKABLES (Press SELECT):

Unlock All Mysteries
94000130 fffb0000
d5000000 00000001
c0000000 00000009
d8000000 020fe525
d2000000 00000000
Press SELECT to Activate

Unlock All Journal Entries
94000130 fffb0000
d5000000 000000ff
c0000000 00000009
d8000000 020fe474
d2000000 00000000
Press SELECT to Activate.

The Hidden Door [No Password Required]
94000130 fffb0000
220fe49c 00000004
d2000000 00000000
Press SELECT to Activate.

MYSTERY CODES:

All Mysteries Discovered (Not Solved)
94000130 fffb0000
220fe726 000000a8
c0000000 000000a7
220fe764 00000001
dc000000 00000002
d2000000 00000000
Press SELECT to Activate.

All Mysteries Discovered & Solved
94000130 fffb0000
220fe727 000000a8
c0000000 000000a7
220fe764 00000002
dc000000 00000002
d2000000 00000000
Press SELECT to Activate.