First of all, to make this easier you will need to go to Options, Gameplay, and turn Increased Stability off. Then, select the Stearman and climb to at least 4,000ft above the ground. Once there, put the throttle down to 0% and keep the plane level till you stall. Hit increase the throttle a bit (35% -40%) and keep hold of "A". This should get you to start spinning. Spin 5 times, then hold D to level yourself and the achievement will unlock.
Note: This can also be completed during the mission Stearman Aerobatics.