You have a grid of heights. You walk from top-left to bottom-right. Each step to an adjacent cell has an effort equal to the absolute difference in heights. The effort of a path is the maximum effort of any single step in that path.
Find the path with the minimum maximum effort. This is not a shortest path by total cost. It's a shortest path by the maximum edge weight along the path. Dijkstra can solve this, but you need to redefine what "cost" means.