Open the Tower of Hanoi puzzle while repairing the robot in the forest. It has four successive boards, and the move limit applies to the combined sequence. Aim to finish below 45 moves in total, rather than spending that allowance on each board.
Select a top disk, then move it to an allowed rod. A larger disk cannot sit on a smaller one. The later boards add colour changes on every move, so the finished stack must also have a single colour. On the two-row layout, horizontal moves can skip rods, while vertical moves stay in the same column.
The first board is the ordinary three-disk puzzle. Number its three occupied-row rods left to right as 1, 2 and 3. Starting with the stack on rod 1, use:
1→3, 1→2, 3→2
1→3, 2→1, 2→3
1→3
For the colour-changing boards, plan the disk's colour as well as its size before moving it. I would watch the complete demonstration below before the first attempt, then pause it at each transfer to follow the remaining exact placements. It shows all four boards and the successful award.
Follow all four boards as one clean attempt. Do not use the red circular arrow as a trophy retry or assume it restores the move allowance. Check the award before leaving the robot, because completing the story puzzle with too many moves is not enough.
If you miss the award, fully close and relaunch the game before beginning another story run. PC players have reported efficient retries failing until a full relaunch. This is a precaution for the replay, not a confirmed PS5 bug fix. Follow the demonstration without extra moves on the new attempt.
External video: complete four-board Hanoi sequence (alphaboot, PC, 26:23)