Running Gun

See above

High Noon

When you choose this archetype at 3rd level,you gain the ability to cast Compelled Duel a number of times per day equal to your proficiency bonus. Your saving throw DC is equal to 8+Prof+CHA.
While a target is affected by this spell, you may use your Sneak Attack when you hit them with an attack

Silver Tongue

Starting at 3rd level, you gain proficiency in Persuasion, Deception, and firearms

Shooting Gallery

At 9th level, your focus during a duel is unmatched. Whenever you reduce a target affected by High Noon to 0 hit points before the spell ends, you may force another creature in range to roll a wisdom saving throw or be affected by the spell for the remainder of the duration.

Additionally, you may now add your Charisma to initiative rolls

Dead Aim

Starting at 13th level, your attacks score a critical hit on a roll of 19-20 on enemies affected by your Compelled Duel

Aim for the Head

At 17th level, you always aim for the head. While your High Noon feature applies to a creature, your Sneak Attack damage against that creature increases by 3d6.