Complex sentence: Affleck won the Golden Globe Award and the BAFTA Award for both Best Director and Best Film (Drama) for "Argo", going on to win his second Academy Award when Argo won the Academy Award for Best Picture.
Split into simpler sentences: Affleck won the Golden Globe Award and the BAFTA Award for both Best Director and Best Film (Drama) for "Argo". He won his second Academy Award when Argo won the Academy Award for Best Picture.