Mysterious Stranger isn't that good an archetype. Sure, it's CHA to damage, but it's in place of the DEX to damage ability he had, and I believe DEX is a more useful ability. Also, pistolero is nice, but actually nicer if you are a single classed (or almost single classed) character, as it's bonuses are spaced out.
Grenadier archetype is almost a must - considering you get Precise Bombs for free with it.
Explosive Missile is actually a freaking awesome discovery, if you interpret it the way I do. Why? Because then you an fire bombs.
Think a bit. What is the second biggest problem of the gunslinger (after reloading time hehe)? Money. At 1 GP each bullet (or more, if you want a fancy bullet) you are shooting gold at your enemies (even tough that depends a lot on how much gold does your DM give you). Now BAM!, you have some free exploding bullets every day. Also, with the right discoveries, they can do stuff (and circuvent another of the gunslinger's weaknessess, which is, the fact that he is mundane). Like blinding or nauseating bombs.
I have a build I've been messing around, based on the concept of an gunslinger alchemist that rides a mammoth with a cannon on its back (but this is optional) for laughs, I'll post it for you to see, tough it uses some 3.5 material too.
I'm posting the complete build for sake of completion. If you don't like the mammoth with a cannon thing (tough I can't see what isn't cool about a mammoth with a cannon), simply remove the level of mammoth rider and take some other archetype instead of Wyrm Sniper. Also, there may be small mistakes on the build, as I have edited it a lot and so, there may be an illegal feat here or there that I haven't found yet.
Human Gunslinger 1/Alchemist 8/Mammoth Rider 1/Fighter 2/Gunslinger +7
Archetypes:Grenadier, Lore Warden Fighter and Wyrm Sniper Gunslinger
1-Point Blank Shot
(Human)- Precise Shot
(Gunslinger)- Gunsmith
(Gunslinger)- EWP Pistols
(Gunslinger)- EWP Cannon or whatever
3-Deadly Shot
5-Rapid Reload
7-Wild Cohort*
9-Extra Discovery
11-Extra Discovery
(Fighter)- Two Weapon Fighting
12- (Fighter)- Improved Two Weapon Fighting
(Fighter) Combat Expertise
13-Extra Discovery
14-(Gunslinger)- Siege Commander
15-Improved Two Weapon Fighting
17-Rapid Shot
18-(Gunslinger)- Signature Deed (Dead shot)
19-Signature Deed (Munitions Master)
*If your DM doesn't like the idea of using Wild Cohort as an animal companion for pre-requisites, substitute for Skill Focus (Handle Animal) and 1 level of Beastmaster.
Don't forget to take Precise Bombs, Explosive Missile and Fast Bombs, no matter what.
The idea is that you either use Dead Shot + Bomb+ Deadly Shot (2 times deadly haha) on your cannon sometimes, and at others your attack a lot of times using your bombs + your pistols. You add both your INT and your DEX on your shots, so have them both really high. And you have a few extracts to have fun with.
EDIT: The Mechanist archetype is also cool, keep it in mind. It uses intelligence for grit, adds extra damage (remember ALL fixed extra damage is applied to your secondary bomb targets) and makes you a LOT better against casters.