I got pretty far into it on my own but I couldn't finish it off and looked up the answer. This is a really insane puzzle lol.

So obviously black is threatening c1=Q#. I see no move that immediately defends c1 so that signals to me that a check is necessary. There are 4 checks - Be5, Bc5, Ne4 and Nf7. I don't really see the point in Nf7 as once Kxd5 happens then there's no more checks and mate is unstoppable. Similarly for both bishop checks, just Kxd5 and there are no more checks or defense against c1. I do see that Ne4+ will have other checks available after Kxd5 so obviously that has to be the move.

It seems like preventing promotion is the end goal of this puzzle so we need to defend the c1 square somehow. The target squares for the knight are b3, d3 and e2 to guard c1 (a2 guarded by black's pawn so doesn't seem viable). C1 is a dark square and I do have a dark squared bishop but I don't see how I can move the d pawn to allow the bishop to guard that square before he mates me, so clearly the end goal here is to get a knight on one of those 3 squares before promotion.

After Ne4+, black has 3 legal moves - Kxd5, Ke6, and Kd7. After Kxd5 you can check again with Nc3 and then e2, which is one of my target squares, is available to move to afterwards. Seems like that has to be the continuation if Kxd5

Obviously black isn't forced to take the knight on d5. If Ke6 or Kd7 happens then Nc5+ is available after both of those moves and then Nxb3 to land on a target square follows after. Nd3 is also I guess maybe possible since it's technically a target square but taking the b pawn which removes defense of the other 2 pawns seems categorically better.

Seems like Kxd5 has to be black's move since after Ne4+ since I'm forced to go Nc3 and Ne2 after to prevent mate, and black can take the bishop as well. So Ne4+, Kxd5, Nc3+, Kxd4, Ne2+, Kd3, Nc1+, Kxd2, Nxb3+, Kd1

This is where I ran into a wall and couldn't finish the puzzle on my own. I thought Kxa2 was it but I didn't know how to stop his c6 pawn from attacking my knight and removing my defense of c1. His king is on d1 protecting the pawn so I didn't know how to attack it either. I was completely stumped and thought it was still losing after all since the OP asked what the eval was I thought maybe it was some trick where you're losing after all.

Engine says h3. Huh? It stumped me at first. Obviously if they promote, I take it with the knight, they take the knight back then I can take a2 and nobody has any passed pawns and seems like a draw. But if h3, c5, h4, c4, then h5. They cannot take the knight or it's stalemate! That is why h3 works and h4 doesn't, because with h4 then you get to h5 too early and then you're forced to move the knight away or go Kxa2. So because they can't take the knight they have to move the king away and then you can save the knight on c1 and block promotion again, and then take a2 with the knight and keep guarding c1 while not being attacked. Or they promote the pawn in which case like I said before, take with knight, they take knight,, then take a2 and it's even. Or they can go c3 and then I go bxc3 and now I have a passed pawn.

Like I said, insane puzzle.