This one is the quickest to get if you're using a guide. You can walk right up to the laser and input the final solution without doing another puzzle in this area.
The Shady Trees area is left of the Keep entrance.
Go in and find the familiar yellow cube that contains the laser site. At the base of it is a puzzle. Even though it is on the other side of the gate you can still solve the puzzle. Just put this in and you're done.
Since it's a little hard to see, here are the instructions, where U, D, L, R are Up, Down, Left, Right.
L1, U1, L3, U1, L2, D2, R2, D1, R3, D1, R1, D1, L1, D1, L2, U1, L2, U1, L1, D2, R2, Down to exit.
The intended way is to go through several smaller puzzles leading up to opening this gate and finally solving it. It appears they let this one slip a little though! Let me know if there are any questions.
Note: You do NOT need to solve all puzzles in the game to unlock the "Challenge" area. So you are fine using this method to get the achievement.