This is very dependent on the surface you intend you device to climb, I mean is it a smooth wall, are there rocks sticking out of it or any sort of holes to grip.
If it is a smooth surface then your best best is some type of suction cup device and possibly a hexapod robot to provide stability. Here is an example of a robot climbing using suction cups
Newlaunches.com - Wall climbing robotIf you let us know the surface then we may be able to help you more.