My father has already quit both smoking and drinking.
Literal
Father [topic-は] already tobacco [also-も] alcohol [also-も] quit-completely [polite-ました].
The も...も pattern emphatically lists items: 'both X and Y.' てしまう here expresses finality — the quitting is complete and irreversible. やめる is the standard verb for quitting a habit. 既に ('already') is slightly more formal than もう.