lv.8-11 bosses gives 1 upgrade mat. + 50% chance of another item (see list from Taon above).
lv.12-14 bosses gives 2 upgrade mat. + 50% chance of another item (see list from Taon above).
lv.15 bosses gives 3 upgrade mat. + 50% chance of another item (see list from Taon above).
you have to calculate or try, how many attacks you need for each lvl. to maximize your rewards.
e.g. if you need 2 attacks for a lvl 15, but only 1 for a lvl 14, then do only the lvl 14 boss.