The flight instructor reported that the student pilot was practicing takeoffs and landings at the airport. The student took off from taxiway Z and flew a right traffic pattern with the intent to land on taxiway A. As the helicopter was making a right crosswind turn over a golf course at 300 ft above ground level, a large bird flew out of the trees and struck the tail rotor. The flight instructor took over control of the helicopter as it began to yaw, and he subsequently initiated an autorotation to the golf course, and the helicopter landed hard. The tailboom and fuselage were substantially damaged. The flight instructor reported that there were no preaccident mechanical malfunctions or failures with the helicopter that would have precluded normal operation. Bird remains identified as a turkey vulture were found on the golf course. The average weight of the species is 4 lbs.