OK

 - The check must come from the knight (D'uh!)
 - The black king must be on c5 for the mate
 - The white king must be used to cover any empty squares to the right of the black king - thus the white king must move, thus there must be at least one non-checking move
 - On a non-checking move Black can try to release the prison by Ra4
 - The only way white can cover this is for the winning check to come from d3, as this covers b4 and the knight can not be captured there (unlike a6 after the rook moves)
 - When white makes the non-checking move he must be in a position to deal with threats from black, in particular the black queen, and checks from the black knight on c7 and the black bishop on h4
 - If on the non-checking move white plays Ke6 directly the knight check from d8 will break the prison
 - Thus the king must go to e4, attracting the black pawn to d5 with check, after which, if the black queen has been eliminated, the white king can go Ke6 Nd8+ Kd7 and it can't at that point be driven away

Putting this all together leads us to

    [Event ""]
    [Site ""]
    [Date "????.??.??"]
    [Round ""]
    [White ""]
    [Black ""]
    [Result "*"]
    [FEN "8/1nq5/bppp4/1p1k1K1N/1rrp3b/2pp2p1/8/n7 w - - 0 1"]
    
    1.Nf4+ Kc5 2.Ne6+ Kd5 3.Nxc7+ Kc5 4.Nxa6+ Kd5 5.Nc7+ Kc5 6.Ne6+ Kd5 7.Nf4+
    Kc5 8.Ke4 d5+ 9.Ke5 Bf6+ 10.Ke6 Nd8+ 11.Kd7 Ra4 12.Nxd3# *

I think that's it, though I can't see at the moment what the Black Knight on a1 is doing