The goal of most climbing walls it to simply get to the top. However, there is no reason not to make the goal something more elaborate.
There is a video game called “Shadow of the Colossus” in which your goal is to guide a man with a sword as he clambers on top of building-sized beasts, with the eventual goal of stabbing the beast in a specific weak point. Secondary goal: do not fall off the beast and be trampled underneath.
The symbol that you have to stab in the game is always some kind of weird looking glowing rune.
Take a normal climbing wall and use a standard LED projector to project a bullseye somewhere onto the wall. The climber’s goal is to clamber over to that target and hit it with their hand. (Or a sword, if the climbing wall is in a country without the legal concept of “liability.”)
Fig 1. A normal climbing wall. The red dots are handholds/footholds.
Fig 2. A projector projects target images onto various locations on the wall.
Alternative scenarios also present themselves, where the bullseye could move around, or multiple ones would have to be hit in sequence.
If extra faithfulness to the source game is desired, the climbing wall could also be mounted on a hydraulic platform that could shake the wall in an attempt to throw off the climber.
A slight modification of this idea would also allow the re-enactment of the scene from The Empire Strikes Back where Luke Skywalker ascends a wire (or rope, in a climbing gym) and throws a grenade inside one of the Imperial Walkers on Hoth. Presumably there are many other movies with suitable scenes. (The climbing of the cliffs in The Princess Bride also comes to mind.)
PROS: Would be amazing. Total cost for non-hydraulic version: only the cost of the projector!
CONS: Might be too amazing.