to catch large fish you must master the double click and hold, fast reel. watch the fish face at the bottom. as soon as the worn out face appears double tap that mouse button. its still hard to get the really big fish in but i hope this gets you the past the large shark challenge. A Blacktip Shark with a shrimp in Biscayne Shelf done it for me.
TOP TIP for catching big fish, when you see the face change on the fish double click and hold for a fast reel. its much easier to get out of the stress zone than the slack zone. took me a long time and much frustration to figure that out.