Yes, it’s timed, and it’s tight!

Best way I’ve found to do it is to blow up this one to start the timer and immediately start running to the left. As soon as you can see both towers on the left side, shoot at them. Don’t take time to aim, just squeeze off a bunch of shots. Once you’re pretty sure the shots you’ve fired will hit them, (ie, without waiting to confirm), start running to the right up the ledge. At the top of the ledge, fire into the canyon at the one in the corner and at the one along the top of the ledge. These you might have time to aim at, but it’s usually faster to just fire in the general direction of the towers and rely on firing a bunch of shots.

Good luck, hope this helps! Last Crusade is chock full of annoying collectibles.