The film begins at Flemner Air Base 20 years in the past. A pilot named Leland "Buzz" Harley (Bill Irwin) loses control of his plane and ejects, leaving his co-pilot Dominic "Mailman" Farnham (Ryan Stiles) to crash; although Mailman survives, he's mistaken for a deer owing to the branches stuck to his helmet and is shot by a hunter. Topper Harley (Charlie Sheen) wakes up from a nightmare he's having about the event when Lt. Commander Block (Kevin Dunn) asks him to return to active duty as a pilot in the U.S. Navy, to help on a new top secret mission: Operation Sleepy Weasel, commanded by the incompetent and oblivious Admiral Benson (Lloyd Bridges). Harley starts to show some psychological problems, especially when his father is mentioned. His therapist, Ramada (Valeria Golino), tries to keep Topper from flying, but she relents, and also starts to build a budding romance with Topper. Meanwhile, Topper gets into a rivalry with another fighter pilot, Kent Gregory (Cary Elwes), a former lover of Ramada and son of "Mailman" Farnham who blames Buzz Harley for his father's death, and believes Topper cannot handle combat pressure.
One night, an American special forces team invades Saddam Hussein's (Haleva) palace and a nearby prison camp to rescue captured soldiers from Operation Desert Storm and to eliminate Saddam, but they find the Iraqis prepared for them, and the entire rescue team is captured. This failed operation turns out to be the latest in a series of rescue attempts which were foiled by the Iraqis, and consequently the advisors of President of the United States Benson (Admiral Benson in the Hot Shots!, played by Lloyd Bridges) suspect sabotage in their own ranks. Colonel Denton Walters (Richard Crenna) suggests to gain the aid of war hero Topper Harley (Charlie Sheen) for the next mission, but Topper has retired from the United States Navy and become a Buddhist in a small Thailand village. Walters and Michelle Huddleston (Brenda Bakke), Central Intelligence Agency, arrive and try to persuade him to come out of retirement in order to rescue the imprisoned soldiers and the previous rescue parties.