You don't say if your friend is a Christian–but if so, she needs to realize that her pride displeases God, and is a sin. The Bible says, "God opposes the proud but gives grace to the humble" (1 Peter 5:5). Arrogance and love are opposites.
First of all, pray for your friend before you speak to her about this. Remember: God can do what we can't do, and He can soften her heart and make her more open to your words. Before Nehemiah asked the Persian king for permission to help his fellow Jews–something the king would normally refuse–he first prayed for days. Later the king granted his request (see Nehemiah 1-2).
Then approach your friend gently, letting her know you value her friendship, and you wish others could come to know her as you have. Sometimes people who appear aloof or arrogant are actually quite shy. Don't rebuke her, but let her know you care. The Bible says, "As God's chosen people ... clothe yourselves with compassion, kindness, humility, gentleness and patience" (Colossians 3:12).
Most of all, point her to Christ. God gave her mind to her, and God loves her and wants her to yield herself–including her mind–to Him. When she does, she will discover the joy and peace He alone can give.