Remember that the previous Beatmania IIDX games have the boss battles? This one has additional bosses for you to deal with. I think that the first IIDX game to feature such boss battles is DJ Troopers where you can attack the bosses while you tap the corresponding notes to the song. By tapping the corresponding notes, you’re attacking the boss but if you MISS, you get attacked back. In DJ Troopers, you can see the health bar on top of the screen and you may want to destroy the bosses completely at the end of the songs so you may have to do very well because those boss songs are already difficult enough. Do it not well and the bosses may survive and your grading for those songs may be affected.
For Legend Cross Mode, it is the continuation of Lincle Kingdom which is the RPG element mode ever since IIDX Lincle. All the songs there are exclusive to IIDX Tricoro but the references can bring you back to the past through the previous IIDX games. One of the songs was previously used in DDR X2 and there’s also the extended version of the song which is assumed to be extra cool. In Legend Cross Mode, you get to make use of your RPG character you’re playing as to attack the bosses shown on the screen while playing the notes to the song. One of the songs has a serious disadvantage to me that the characters shown on the screen don’t happen to look like the bosses so it’s kind of pointless to call that song a boss song.