Climbing a block in 2d

Hi all, I'm stuck with this problem. I'm making something like a 2d platform game but in which some AI characters could be able to climb blocks like this. (the left one). And also the block and the floor where both are (the block and the character) could be moving, so I guess I cannot just translate my character to that position.

So I already have the trigger to start climbing, but I cannot figure out how to make my character climb a fixed height. I'm now trying coroutines without success.

Any idea how to do this? Thanks in advance!