This could use a bit more explanation. For instance:

How many points and how many bonus moves do you get for a capture? Does it depend on what you capture? (It looks like it's one bonus move whatever you capture, but more points for more valuable pieces; 1 for a pawn, 3 for a bishop, so I'll guess it's 5 for a rook and 9 for a queen.)

Does "Beware of attackers!" mean (1) you aren't allowed to move the knight to a square that's attached, (2) you will get some points deducted when you do, or (3) nothing, it's just flavour-text? (It looks like it's #2, a loss of one point each time you move to a square that's attacked.)

The instructions don't mention the "clean board" bonus; I think they should.

I'd write it something like this:

Complete each level by reaching the target within the given number of moves.

Each piece you capture gives you one more move, and points according to the value of the piece.

You lose one point any time you move to a square that's attacked.

Your score for the level is the number of moves you had spare at the end, times the number of points you earned. Double if you captured all the pieces!

(... Except that it looks as if there's some further "streak" mechanic, which I haven't tried to figure out the details of.)

If that's too long, put it behind a clicky-button, and just say "Get your knight to the target square. Earn points for getting there quickly without being attacked, and capturing pieces on the way." plus a button labelled something like "Full rules".

Maybe make the notification when you capture a piece say something like "+3 points / +1 move"?

If the levels get fairly crowded then it might be expensive to get the computer to find the best possible score, but it shouldn't be hard to make it find a pretty good score. You could present that, either at the start or after the user finishes the level, as a target, and congratulate them when they meet or even beat it.