Drillneck is a quiver that is very powerful for a lot of different builds in Path of Exile. It can drop from pretty much any mob from around level 35+, but it is also possible to farm it by finding Divniation Cards.
The div cards for Drillneck is called The Fletcher, and can only drop from a Unique mob called Ironpoint the Forsaken on Cruel and Merciless difficulty (and also from Lieutenant of the Bow in Lab). You need a total of 8 of these to get a Drillneck. Ironpoint the Forsaken is located in The Climb in Act 1, and luckily he is pretty close to the waypoint.
To farm The Fletcher, use the waypoint to The Climb, run until you find him, kill him, TP back and go again. It is far from the most exciting grind, but the cards are not very rare, so you will get it pretty fast.
It is important to remember that The Fletcher only awards a corrupted Drillneck, so if you want an uncorrupted one, you need to have luck and get it as a random drop.