For covering huge distances in the quickest time possible use Batman's Grapnel. This valuable gadget lets you zip between buildings, and also comes in handy for neutralizing snipers, or simply dragging a bad guy into the Caped Crusader's clutches.
Always take out armed thugs first. Also when in a fight deflect incoming attacks by pressing the counterattack icon when the virtual button appears on-screen.
Dead bad guys leave credits behind always pick them up.