Pinsir can only be found in one location, and 6 badges in you may not be looking for teammates. But should you have room for this classic bug, it won't let you down. Bug is an excellent typing to take on a good portion of Team Magma and basically all of team Aqua, and Pinsir gets good coverage from its movepool as well as TMs.
Gym #7 - Tate and Liza (Mossdeep City, Psychic-type): Not surprisingly Pinsir can take out basically every gym trainer with one hand tied behind its back. Once you get to the leaders, though, you have to deal with their lovely secondary typing... Rock. However, Lunatone can be outsped and OHKO'd with X-Scissor due to its lower defense (assuming matching levels). Couple that with a partner that can take out Solrock and your opponent may never get a chance to attack. Even if your partner can't handle it, Solrock can't OHKO with Rock Slide unless it rolls high damage and crits, and with a couple of levels over it Pinsir is completely in the clear. Unless Pinsir meets its untimely death this battle shouldn't last more than two turns.
Maxie/Archie (Seafloor Cavern): Mightyena is almost too easy with an X-Scissor, and if you set up a couple Swords Dance here you might be able to sweep. Muk will give you the most problems since Bug and Fighting won't help you, but if you've got Rock Tomb you can at least do neutral damage; beware of its Poison STAB, though, especially if it happens to inflict Poison status: it could chip away Pinsir's remaining health if it's already weakened. Crobat will fall to a buffed Rock Tomb, but you WILL be outsped and tanking supereffective STAB Acrobatics is no fun, so stay away unless you absolutely have no better options, or Pinsir will be at a serious risk here. Generally I'd say let Pinsir take care of Mightyena and switch out, but if you're determined to sweep it is possible. Also note that after you get dive you can find Pinsirite, so you can also Mega evolve for this battle to buff those stats farther.
Gym #8 - Wallace (Sootopolis City, Water-type): It is fairly easy to set up on Luvdisc and sweep Wallace, as long as you don't hit yourself in confusion from Sweet Kiss. Maybe equip a Berry to combat that, or bring Full Heals, and get yourself set up. Mega Pinsir has more than enough Speed and Attack to OHKO everything with a couple of Swords Dance under its belt, possibly even just one; so as long as you can grab some luck against Luvdisc, this battle should be a breeze.
Wally (Victory Road): Pinsir shouldn't really be your lead unless you're way overleveled (possible if you've had the exp share on for a while). Altaria's Aerial Ace will do decent damage, but you can counter with a nasty Rock move of choice (Rock Slide if you went and got it before). Once you get to Delcatty you can Bulk Up or Swords Dance and get ready for a sweep, just make sure to heal as needed. Delcatty will fall to a Brick Break or Storm Throw, Roselia can't stand up to STAB X-Scissor, and you'll be faster than Mega Gallade for the neutral X-Scissor as well. Magneton will get a hit off because of Sturdy, so make sure you're healed up there, especially if you went Mega and are thus weak to Electric. Mega Evolution is actually discouraged until Gallade for this battle, to avoid a super effective Discharge from Magneton.
Elite Four Sidney (Ever Grande City, Dark-type): This battle is a joke for Pinsir. Depending on levels you may not even need to set up. Just Mega Evolve, maybe throw in a Swords Dance for good measure, and have at it.
Elite Four Phoebe (Ever Grande City, Ghost-type): Pinsir's Bug and Fighting coverage have basically nothing to offer in this battle, so a normal Pinsir should stay out of it. However, a Mega Pinsir is more than capable of taking on Phoebe: Aerilate-boosted Return deals a good amount of damage to most of her Pokémon and, barring Will-O-Wisp burns, it should be able to knock out everyone on her side of the field except Dusknoir, which should be avoided due to the elemental Punches.
Elite Four Glacia (Ever Grande City, Ice-type): There's no scary coverage here if you don't Mega Evolve Pinsir, and a good strong Brick Break/Storm Throw should get you going places. Just keep Pinsir healed and DON'T go Mega, and you can have a sweep on your hands.
Elite Four Drake (Ever Grande City, Dragon-type): There are some scary coverage moves lurking in this battle, especially if you Mega Evolve and gain weaknesses to Electric and Ice. In fact, every single dragon will threaten you. And even if you don't, you're once again facing STAB Aerial Ace from Altaria. You can set up in the face of it if you're really overleveled, but otherwise just sit back and let someone else do the work here.
Champion Steven (Ever Grande City, Steel-type): Just like Drake, you're facing off against STAB Aerial Ace if you lead with Pinsir, this time from Skarmory. And this time, both your Rock Coverage and Fighting move will only do neutral damage. Beyond that, there are a whole lot of rock moves in this battle, Many of them STAB. And Aggron can't fall in one hit no matter how much you set up due to Sturdy. Pinsir can get some KOs in this battle, but it's generally not worth the risk unless you're desperate. Mega Metagross will take moderate damage from neutral X-Scissor if you must use Pinsir.
Post-Game: Chances are the many Dragon-, Flying- and Fire-types will give Pinsir a hard time. Tread carefully.
You'll get Pinsir with Brick Break, Double Hit, Vital Throw, and either Submission (level 30) or Revenge (level 28). Slap Bulk Up on there at once over your least preferred Fighting move, and I personally like the coverage of Rock Tomb as well, probably over Double Hit or another Fighting move. X-Scissor, Pinsir's only STAB move by level up, comes mercifully at level 33, and will round out your moveset with the aforementioned Bulk Up, Rock Tomb, X-Scissor, and probably Brick Break. Beyond that only a few level-up moves are worth mentioning. Storm Throw can be taught over Brick Break at 36, breaking through any defensive set up the opposing Pokémon is using and dealing more damage than Brick Break without a crit. Swords Dance at 40 can replace Bulk Up depending on personal style. Thrash isn't worth losing coverage, and Guillotine is not at all reliable. Superpower can be taught, but generally setting up and buffing all your attacks is more reliable than reducing your own with a super-charged move.
A couple of TMs have already been mentioned. Rock Tomb is great until you can access Rock Slide. Bulk Up and Swords Dance can basically be used interchangeably depending on the circumstance. Dig and Earthquake are worth mentioning, and can also be swapped out with Rock coverage as needed. In fact, after Victory Road where you get X-Scissor, Pinsir's entire moveset can be made up of TMs if you stuck with Brick Break, giving it loads of flexibility between battles. Thief is the last TM worth mentioning, as it can be used to combat Phoebe if necessary. If you happen to find Pinsir with an egg move, not a lot actually changes. You still have the same types covered as you would with TMs. If you use Mega Pinsir often, remember that Return is an amazing move to have, thanks to the ability Aerilate; it's more powerful than Acrobatics.
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
What Nature do I want? Anything that reduces Special Attack is the best option. Speed and Attack raising natures are also decent regardless of what they lower as it helps with sweeping potential.
Which Ability do I want? Moxie, of course, is the best of the lot. However, it does require DexNav usage. If you can't have Moxie for some reason, both Hyper Cutter and Mold Breaker will do fine; neither is particularly useful, though Hyper Cutter does save you from Mightyena's Intimidate shenanigans when needed.
How good is Pinsir in a Nuzlocke? More useful than expected, and quite physically sturdy as well. It has key matchups against the evil team leaders and Sydney's Dark-types, and Liza and Tate's Psychic-types that can give it a good spot on the team late game.