D&D 5E Best archer build?

[Bardbarian]

If you are looking from a pure combat perspective nothing beats the fighter. battle masters in particular are excellent for precise shot however other fighter options perform well. Other options such as ranger, rogue and even bladelock can do well but none are quite as good as the fighter from a pure combat perspective. When you decide there are other aspects of the game that interest you such as defense, control, and versatility, then the other option become more appealing. Personally I like 11 fighter then add in sorcerer for quickened metamagic for an example of versatility. Optimization will matter greatly when you know what level you expect to play at. some builds are stronger at low levels while others are late bloomers and will seem weaker early on but be extremely powerful when facing the types of challenges faced by characters who can solve their problems with a wish. In the end, you need to decide what your actual play goals are. Focus or balance? Theme or mechanics? If your idea of the best archer is a master diplomat then much of the advise you'll get wont help you very much. Once you set your expectations the community can be a better resource.

 

[Zardnaar]

There is no way ranger is better than battlemaster if you are talking sharpshooter

Hunter Ranger is with hunters quarry spells and colossus slayer and/ore hordebreaker. Vs action surge the Hunter ranger comes out ahead until level 11 or so. They both get the same amount of attacks except hordebreaker triggers quite frequently giving the hunter an extra attack more than the fighters action surge which they might get to use 2 or 3 times a day (vs 1d6 all the time+ and etra 1d8 or attack fairly frequently).

Fighter hits 20 dex at 6 instead of 8 though.

I suppose fighter might win with the hand crossbow thing at a few levels (which rangers can also do and take hordebreaker with), but good luck getting a magic hand crossbow I don't think a single WoTC adventure has one but I have seen magic longbows.