You can prototype this without animations, as it will generally require you to move the capsule to certain directions. Only after that you will make this look cool with the well setup animbp
If you go with the character movement component, set it to flying mode so you can have more freedom regarding where to move the capsule. You can also enable the rendering the capsule in game mode (uncheck the hidden in game) that helps you to see what is going on. Since the Z axis movement (climb up the tree) only required when you actually want the squirrel to go up, you can enable this flying mode upon requirement only, so you can switch back to walk mode and have Jump feature and others.
With lots of work, obviously
This image should help you to setup the move up feature with a tpp character: