1. "I wouldn't like to be in his shoes." means "I wouldn't like to be in his situation".
2. "He keeps beefing about me to his parents." "Beef" means to complain.
3. "I'm planning to beef up some money." I'm not really familiar with this one, but "beef up" in general means to increase the size of something.
4. "...it's not my cup of tea." means "It's not something I enjoy."