Anna is heavily mechanised, like her fellow agent Gunther Hermann, and runs the stealth section of the UNACTCO training ground. Whilst she is not as eager to engage in full frontal combat, like Agent Hermann, she does appreciate the elimination of enemy combatants. If you use a non-lethal approach in the early missions, Agent Navarre will chastise you for being too lenient.
There are two point in the game where you can fight Anna Navarre.
The first one is rather early on when you are sent to arrest Lebedev in his private jet at La Guardia. You will find Lebedev after you have spoken to your brother Paul who informs you that he has been working with the NSF. You'll spend some time talking with Lebedev as he tries to turn you. After the first conversation ends Anna will barge in. She will order you to kill Lebedev, at which point you can also open fire on Anna and kill her. You'll have to be carefull not to kill her too close to Lebedev because Mechs explode when killed! Now Lebedev will be glad to see that you turned and tell you someone will contact you.
If you did choose to kill Lebedev or simply let Anna kill him, then there'll be a second point where you will have a chance to kill her during your escape from UNATCO-HQ. The easiest way to do it is by hacking several computers around the base before you proceed to the exit. On two of these computers you will find two parts of her Killphrase. Once you have found them you will simply tell Anna "Flatlander Woman" and "boom"! You can, of course, opt to just shoot her.
When Anna is dead Gunther Hermann will have a serious beef with you. Not immediately if you pick the first chance to kill Anna, because they'll assume something went wrong on the plane. Eventually though Hermann will catch up and he'll be in a very foul mood!