Instructions
Fly over the missile dispenser as Batman in the Batwing to stock up on missiles you can use to defeat the Scarecrow. Scarecrow's biplane follow yous, making it impossible to land a shot directly.
Switch your active character to Robin in the Batcopter. To hit the Scarecrow you have to immobilize him, so follow behind him and target Scarecrow's biplane with the tow cable of the Batcopter.
Switch back to Batman in the Batwing once you catch the Scarecrow with your tow cable. The tow cable keeps Scarecrow's biplane from following you, so loop around and fire a missile at the biplane before the Scarecrow escapes from the cable.
Switch back to Robin in the Batcopter. Follow Scarecrow's biplane again, capturing it with the tow cable when you get a chance. Immediately switch back to Batman in the Batwing to fire another missile.
Alternate between Batman and Robin, catching Scarecrow's biplane with the Batcopter's tow cable and then firing a missile at it. When you hit the biplane three times, the Scarecrow is defeated, resulting in Batman and Robin capturing him and sending him to Arkham Asylum.