The "secret boss" can only be completed during a specific point in Route B. You can also be locked out of it if you miss it. After talking to Evangeline for the first time, you have to immediately run to the manhole in the Living District next to the music studio. The moment you enter into the basement of the Library, you will be locked out.
Stats are generally straight forward. Skill attack affects skill damage. Luck doesn't really affect critical damage either. Luck primarily focuses on status effects and debuffs. Defense will increase the amount of damage you can take, but keep in mind, certain bosses can have attacks that ignore defense.