In order to win this achievement, you'll have to defeat Boss 1 and Boss 3 at their maximum level which means facing Faintear. If you managed to beat her twice, you won't have to worry again about continues or lives, you will face another form of the last boss of the game and you will earn this achivement when credits roll is finished. Of course as title implies, you'll have to do it with Exelica.
Edit: At the moment, it's still unclear whether continues impact this achievement or not.
DarkSephiroth07 added: "Just to correct this, you have to get 3000 metals for the first Faintear in stage 1 and 2900 metals for the second Faintear in stage 3." He also added that you're not forced to go by the default settings. Make those extra lives and bombs count!
Ask for more details if need be.