Requires opening up the transmission, it won't be cheap to have it repaired!
Syncro's are what allow the engine and transmission to be rotating at different speeds and still have the car go into gear without grinding or doing damage to the transmission. In the days of old before cars had syncro's in the transmissions, people would have to rev match between shifts in order not to grind gears.
One thing you can try that might prolong the necessary repairs is to change the fluid to a high quality one like redline mt-90 or royal purple. Some people have success with GM synchromesh, but none of it is cheap. Albeit, much cheaper than replacing/rebuilding your transmission