Okay here it is:
Battle pike:clear 21 rooms to face Pike queen Lucy= luck symbol
Battle Dome:win 5 tournaments without losing anface Dome superstar Tucker=tactics symbol.
Battle pyramid:complete 21 floors and face Pyramid king brandon.
Battle Arena:win 21 battles and face-------.
Battle palace:win 21 battles and face palace----spencer.
Battle Tower:win 21 battles and face salon maiden Anabel
Battle factory:win 21 battles and face Factory head Noland.
sigh, I always manage to lose on the 21st battle in Palace, Tower,
and arena.If you defeat the Leader you get a lot
of battle points.
Okay, hope this helps!