You need a good trial lawyer to cross-examine them on prior istatements, confront with differing evidence, impeach their character, motive to lie, etc. Your criminal defense attorney with trial experience will know how to do this.
I am trying to give you a general answer to your question. We do not have an attorney-client relationship by this response on the avvo website. I have not been retained to represent you. I am licensed to practice law in Kentucky and in federal court in this state and the Southern District of Indiana. You need to seek legal advice from an attorney licensed to practice in your area..
Effective cross examination while the person is under oath is an exceelent way to show a lie.
It takes years of skilled practice to master the technique. Those of us that know how sell that skill as our career of being a lawyer.