The best way to keep tuna burgers from falling apart is to ensure you compress the patties together tightly when forming them. You don't want the patty too big either; 3-4 inches in diameter is the ideal size for a tuna patty. When you're cooking the tuna patties, make sure the pan is hot (medium-high heat) before you add the patties and let them cook the entire 5-6 minutes on each side (do not try to flip them too early) and flip them over carefully with a large, wide, thin spatula.