The Secret Mission achievements do not unlock until after the battle so you must successfully complete the secret requirement, then win the battle. If you do not see "Great!" and the battle take a small timeout to show the aftermath of your deed, then you have not done it correctly. Make sure you do all of these in a single playthrough! Doing so will unlock the "True Knight" title for Yuri which you will need for the "They Call Me..." achievement!
Stick close to Zagi and keep pummeling him with normal attacks. The more damage you take, the more healing Estellise will have to do, so she will stay out of the fray. She took two Cyclone attacks and I was able to get this, so I'm not sure what the exact cutoff is.