How to break out the direction lines of an anchor point in After Effects?

On a Mac, it's Option + Shift + Click to cause the bezier levers to control each side independently. 

you probably mean break the bezier curves of a motion path, correct?

you can activate the convert vertex tool and us it on the handle

either of these will do:

• manually by picking the tool from the tools menu
• if you set the preferences to not toggle between mask and feather tool, by using the G shortcut a few times.
• with the pen tool active press Alt (on Windows) and click and release.
• with the selection tool active press Ctrl+Alt (on Windows) and click on the handle and release

Hold down the Alt key when you have the pen tool selected to toggle to the Convert Vertex Tool. If you have the selection tool active use Coomand/Control + Alt

hope this helps

Angie Taylor