Which nozzle should I buy for Anycubic i3 Mega? I'd like to buy a new nozzle for my Anycubic i3 Mega because it's not precise enough - it fails to print small details like 1&nbsp;mm eyebrows.

Currently it has a 0.4&nbsp;mm nozzle and I'd like to buy a better one but I don't know how to choose one which is compatible with this printer.

If you have any advice, please let me know.
According to Anycubic this printer uses the E3D V5 type hotend as can be seen from the linked video of the AnyCubic Mega:




The brass nozzle you see is fully compatible with the E3D v6 nozzle and can be found on those typical auction and Chinese websites by looking for "E3D nozzle". They are also available from E3D directly, the designer/creator of the E3D hotend family, and other specialized manufacturers like the Olsson Ruby. These nozzles have a short nozzle (snout) and are screwed into the heater block with M6 threads.1)



The smaller the diameter, the smaller the filament traces and the higher the print detail resolution. Note that a smaller diameter causes thinner walls for the same amount of (vertical) walls and may require additional perimeters to get similar strength and rigidity. The maximum layer thickness also decreases, as prints with a layer height above 75 % of the nozzle diameter have very poor quality. As an example, a 0.25 mm nozzle should not print layers thicker than $0.75 \times 0.25\text{ mm} = 0.19\text{ mm}$. 

As such printing with smaller nozzle diameters increases print time. Also note that a smaller diameter requires more force to push the filament through and could use some extra temperature to make the filament more fluid or reduction of the print speed.

Just buy some spare nozzles of different nozzle diameter and experiment what works best for you.

1) - The other popular style of M6 threaded nozzles has a long body and long taper (often referred to as MK8 nozzle; they come in two different shapes). While these might work, they extend from the heater block considerably further and might need readjustment of the heater block (as explained here):