Have you checked out this tutorial yet?
https://www.scirra.com/tutorials/1115/a ... latformers
One thing you can do is have triggers set all around the environment that change the character's 'state' as it approaches an obstacle or ladder or such. For example, a jump trigger on either side of a pit, or a climb trigger at the base of a ladder. The jump trigger would of course active the jump action, and the climb trigger actives the 'Climb' state, which plays the climbing animation as they move up the ladder, as well as whatever climb behavior you have set, so long as the character's state is currently set to 'Climb.'
If you click to the right of the character, and they're not on a ladder or in the middle of a jump, you start the 'Right' state, in which they continuously simulate right movement. Ditto for clicking to their left and activating the 'Left' state. If they're about to walk over a pit, there should be jump triggers there that make the character automatically jump once it collides with them.
That would work for very simple cases, step by step or trigger to trigger, but it wouldn't work in more advanced cases. For example, in this case:
You can click on the checkmark, but since the ladder is to the character's left and the right-ward click means the 'Right' state has been activated, the character wouldn't properly reach the climb trigger to go up the ladder. You have to figure out what the next step is (the ladder) and click on it, and once you're up the ladder think about the next step (go right) and so on.
I suppose to go more steps ahead automatically, you'd need to make these triggers perform double duty as waypoints. Here's a bit on that from the same guy:
https://www.scirra.com/tutorials/1113/a ... -waypoints
Not entirely sure how to implement that, aside from having every waypoint know what path needs to be taken to reach any other waypoint. Hopefully someone has an easier solution for a more advanced pathfinding.