How long does Achilles tendon rupture need to fully recover?

About 6 months. Assuming surgical repair and 8 weeks of casting, it will likely take about 6 months but up to a year for full recovery.
8-10 weeks. Usually a complete tear will require about 8 weeks to heal after it is repaired surgically after that it may take another 4-6 months of rehabilitation to regain motion, strength and gradually return to running and sporting activities.