The "Battlefield Experience" path feature simply gives you more options for what to shoot and still gain the bonus damage.
The way I read it, it's a minor action to quarry each one and you can only apply quarry damage once per round (to a single target).
Seems pretty straightforward to me. Also, just like Sneak Attack and Warlock's Curse, the quarry text includes "once per round", which implies it has the same limitations, which makes sense. After all, damaging multiple enemies at the same time with striker level damage is the Sorcerer's shtick, not the Ranger's.PHB FAQ said:28. Does the battlefield archer’s Battlefield Experience paragon path feature allow me to designate more than one creature as my quarry with one action?
No. This path feature allows you to have more than one creature designated as your quarry, but it does not grant you the ability to designate multiple creatures with a single action.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.