The engine running on the judge is a modified version of PZChessBot at depth 7, using only HCE for evaluation. The judge takes a negligible amount of time per move.

Implementing move searching is not hard, but searching moves and evaluating positions quickly is.

Speed optimizations, most-to-least useful, with approximate difficulty to implement

• Alpha/beta pruning (very easy)
• Late move reductions (very easy)
• Zobrist hashing and transposition tables for cutoffs (normal)
• Move ordering using transposition tables or MVV-LVA (easy)
• Null-move pruning (easy)
• Bitboard or hybrid as opposed to mailbox-only (hard)
• Principal-Variation Search (very easy)

Strength optimizations, most-to-least useful, with approximate difficulty to implement

• NNUE (insane, the hardest part is fitting the model into the submission size limit)
• Quiescence search (normal)
• Fine-tuned evaluation function (normal)
• Tactical motif detection (hard)

Note that optimizing speed has the effect of also optimizing strength, since you can search at higher depths!!

You may also find the Chessprogramming Wiki helpful.