Somewhat contrary to the challenge description, you need to get an "A" rank or better. This is the total rank for a mission, rather than for the individual mission objectives.
A Blackbone at any evolution with a max-level wingman, preferably a Blackbone Radiance or a Silvertail Radiance, can easily "S" rank the Lava Lake stage "Thinning the Herd". This level contains nothing but fire-elemental enemies, so the Blackbone and Silvertail's lightning attacks deal extra damage.
It can be helpful to feed the Blackbone to teach it a vision attack, such as "Roar Photon".