A complicated Mini Forest puzzle

PGN4:

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[Variant "FFA"]
[RuleVariants "CaptureTheKing EnPassant PromoteTo=BCFGIS"]
[CurrentMove "0"]

Difficulty: Hard.

Themes: Endgames, Zugzwang, Switchback, Domination

Please note that there exists only one solution, everything else allows black/yellow to draw / win.

White/red to play and win.

It;s quite hard but lemme see...

assuming the lower left corner is a1 and the upper left corner is a8, a good start is...

1. Ig5+ hxg5

2. Cxg5 ...

This attacks the grasshopper and checks the king on different moves.

The following line just gives black/yellow a trivial victory, with red being able to do nothing.

I was looking at rerouting the camel to bring it into the game and to ultimately dominate the enemy king by taking away squares, forcing it into zugzwang (like the themes you mentioned in the description). Here is a line I found:

1. Ck5-h4 .. Ie11-g9
2. Ch4-e5 .. Ih8-f10
3. Kf8-e9

Cc5 is the threat and yellow does not have any moves to stop it, except for Gc3. The problem is when you reach a situation like this:

While white/red may have just won an alfil, it is incredibly hard for them to make progress, so much to the point I might even consider it impossible for them to win. That's how strong the grasshopper is on c3. The camel is tied down to the defense of the e3 alfil, and if the alfil ever moves, the pawn starts moving right away. Red will have to bring the other alfil back and play a very passive position with little chances to win, and the game will most likely end in a draw* by repetition of some sort (provided yellow doesn't throw for some reason). 

*One of the many lines:

1. Ck5-h4 .. Ie11-g9
2. Ch4-e5 .. Ih8-f10
3. Kf8-e9 .. Gk11-f6
4. Ke9xIf10 .. Ig9-i7
5. Ih6-j4 .. γk9-j8
6. Ig7-i5 .. Kh10-i9
7. Ce5-h4 .. Ki9-h8
8. Ch4-g7 .. Kh8-i9
9. Cg7-j6+ .. Ki9-h8

So I took some time to look at another line:

1. Ck5-h4 .. Ie11-g9
2. Ig7-i9 .. Kh10xIi9
3. Kf8xIg9 .. Gk11-i11
4. Ch4-g7

In a position like this, the grasshopper is completely blocked off, the pawn can't move without being lost, and the king can't move without giving up the alfil. The alfil itself can't move because Cc7+ forces yellow to play an incredibly passive position:

Black/yellow has one move that doesn't lose the game on the spot, which is Kg7, allowing the red king to get into e7, forcing the grasshopper back, and end up in a dominant position, albeit down one point.

So far so wrong, but you are on the right track. Remember that themes includes "Tempi play", you need to find a way to lose a move and get equal on points simultaneously, and that's very complicated here.

You allow yellow/black to get activity, while the only winning line includes sacrificing material for a surprise checkmate or winning a grasshopper.

As per the image you posted, you need to find a way to enter it having both alfils, not just one, and it being white to move and not black before.