At the end of every level, you will fight a member of the 10 Suns which are the bosses of the level. As you go through the game, the bosses will be harder and harder with the later bosses having more forms and you doing less damage to them. To unlock the "boss" achievements, you have to destroy the bosses at the end of each respective stage. All boss achievements can be achieved in 1 playthrough assuming you're playing on slash mode. This is because stage 5 is not present in origin mode thus the Nazuna of the 10 Suns achievement is unobtainable.