The beatitudes outline what happens in a person's heart in conversion. But the fullness of the beatitudes consists in its application to heart purity.
As in conversion, the path to entire sanctification begins with poverty of spirit. You begin to see the disparity between your walk and the apostles' walk. Every area of your spiritual life–the music, sermons, prayers–seems poor.
This leads to mourning, then humility. A hunger and thirst for righteousness clamor in your heart. An intense longing to be like Jesus consumes you. You see that you must either be made like Jesus, or go to hell.
Finally, you become merciful and pure in heart. Now, you become a peacemaker and testify to the work of Jesus in your heart. This testimony will result in persecution–but you will respond with rejoicing!