Chivalry 2

The quickest and easiest way I have found to get the 100 Archer kills is once you have unlocked the Crossbowman class which is unlocked once hitting level 4 as an archer. To fire an arrow simply Hold for accuracy and press to fire the arrow itself. Pressing again will reload your crossbow.

Next I would say the best current mode for this is the 40 Player Mixed modes as it has less players and more AI on each team. The reason this is significant is because AI will die in one hit anywhere and from any range of a crossbow but not of a bow and will still count towards your achievement. AI are also easier to hit as they don't move as much. The only other advice I can offer is this

1) Try to keep the high ground
2) Stay near Ammo crates
3) Make sure you are behind your teammates so that you don't get rushed
4) The further away your opponent is the higher you may have to aim above where they actually are
5) Try to aim for enemies with less health such as AI, footman, enemy archers or even bloodied enemies.
6) headshots deal extra damage

Update: Currently this achievement is glitchy and only counts kills done with the base Archer class with the bow. Hopefully they fix this

Quick Edit: As stated by one of the commenters and forgotten by me, all kills with your melee weapons as this class also count towards your achievements progress and comes in handy if you're being charged at just simply press and you will be able to use your secondary for melee combat.