Paul's zeal was his enthusiasm for honoring God. He believed that by persecuting the church he proved how zealous he was for God. Alternate translation: "I had so much zeal for God that I persecuted the church" or "Because I wanted so much to honor God, I persecuted the church"
"Righteousness under the law" refers to being righteous by obeying the law. Paul obeyed the law so carefully that he believed that no one could find any part of it that he disobeyed. Alternate Translation: "I was so righteous by obeying the law that I was blameless"