A few ideas:
1. Check for logs in your eye before you go pointing out splinters in someone else's eye. We are all hypocrites because we are human beings (the only exception to that rule being Jesus Christ) and we are all imperfect witnesses, so there is always going to be some level of hypocrisy in your life because you are constantly fighting your sin nature. Regardless, be ready for the confronted person to start throwing accusations of hypocrisy against you as a self-defense mechanism and in an attempt to (unsuccessfully) deflect the conviction of the Holy Spirit.
2. A strong negative reaction from the person is a good thing, because that's usually the first sign that the Holy Spirit is convicting that person. They may be fighting it, which is why they get angry, defensive, irritated, accusatory, threatening, etc., but the Holy Spirit will continue to chip away at their conscience over time.
3. I definitely agree with the pick your battles sentiment, EXCEPT in cases where this person is in a leadership position in the Church. If they are a pastor, deacon, elder, whatever, then you NEED to confront them. If they are a mature leader and a mature Christian, then they should welcome the confrontation. If not... well, refer back to #2.