Actually you aren't trying to beat Sylvie, you are supposed to defeat the NM Burgeoning Flames that spawns as a result of the Quest that you trigger with the NPC Sylvie. I will paste the walk thru page for the Quest named Elementary, My Dear Sylvie below and will also paste a link for the NM Burgeoning Flames. There is a testimonial page at the bottom of the Burgeoning Flames page where other players have given accounts of how they approached the fight that may help you.
I revamped my last answer after dgoing some research. The input by Blue Donkey Kong I would say is solid. He is a daily poster on the FFXIcolpieda.org site under multiple categories. The 2nd poster gives very detailed advice, which I always like to see. The sad fact of the matter is that not a lot of info has been put in ANY database regarding the Burgeoning Flames. I went to Google and got only 4 hits. Sorry. If you have info or strategy to add after your fight, PLEASE create an account and add your testimonial to help other players in the future. Skyfiredancer (talk) 05:16, May 24, 2015 (UTC) http://ffxiclopedia.wikia.com/wiki/Sylvie