That one is Rise to the Challenge.
In Lyn mode, that song is heard when you fight Lungdren. All the other bosses are Attack Now.
In Elliwood/Hector Mode, Rise to the Challenge is played when you fight a boss that isn't one of the Four Fangs of the Black Fang.
Lloyd, Linus, Sonia, and Limstella's boss fights music is Softly with Grace.
When you fight other less-important bosses, e.g. Uhai, Jerme, Kenneth, Oleg, etc. you listen to Rise to the Challenge.
I like that song too. ^^