Bouncer missions are first unlocked in Chapter 5. Head to the east side of Theater Square and a man will ask you for help. The bouncer missions are located in Debolah, located just on the west side of Theater Square and down the stairs. The achievement will pop after completing all 26 missions on each of the three difficulties. Successfully completing a mission will unlock that same mission on hard difficulty (except the last 3) and the next mission. Completing on hard will unlock it on legend. The last 3 missions will have hard mode unlocked when all 23 previous missions have been completed on hard and legend respectively.
Whilst you have full access to your equipment (gear and weapons) you have no access to your inventory so unfortunately there is no way to heal during the mission. Drinking a drink from a vending machine for its +attack or +defense bonus can help but will run out quickly.
I wouldn't recommend going too far until you've beaten the game, the first 23 are straightforward and the last 3 are still doable, it's definitely best until you've maxed out your character and finished the main story so you can purchase post game only weapons from Kamiyama in Tenkaichi Alley. Namely the Dragon SP pistol and the Photon Blade RG, both are infinite weapons. If you don't want to wait until post game, give Kamiyama 5 mil in weapon and armor sales for the ability to buy the infinite Illegal Poison Kodachi for 5 mil and buy the 3 Transcendent pieces of armour.
I'd recommend going through the first 23 missions first on normal for the gear rewards. Namely the mission An Explosive Plot gives you the Replica Sacred Wood Armour (if you didn't buy during chapter 16), a few missions later The Sex-starved Samurai gives you the real Sacred Wood Armour. These automatically block incoming bullets for you which can be a life saver. The last three missions give you the Dragons Binding, Dragon God Amulet and War God Talisman respectively. A sacrifice stone can be handy in a pinch and all will be important for the legend missions.
Wearing Dragon's Binding, Dragon God Amulet and Eye of the Dragon (from Dragon Palace) will give you a gear bonus of evasion and weapon resistance and is incredibly helpful. The Sacred Wood Armour, Payback Ring (More damage when at less health) and War God Talisman (slowly raises heat) can be subbed in for some missions. The Dragon Pistol SP is amazing for just spamming Y (not RB and Y since it's slower) and almost stunlocks enemies. The next two slots should also be infinites, I believe the photon weapons do more damage to Amons when their shields are up in the last 3 missions.
The last 3 missions are the difficult ones here, the first two feature a ridiculously tough Amon and the last features 3 of them! One tip I can give is going into the pause menu and switching difficulty to easy. Despite the mission difficulty (Which all that changes is damage you cause and take from the same enemies) it still is based around the overall game difficulty and easy just makes it so much more manageable.
Between a Rock and a Hard Place - This features 3 sets of enemies. The 1st is slow big guys who take a lot of damage to take down but move so slow it's simple to spam the pistol and heat with it when they get close. 2nd wave is has a few guys and 2 bosses. Spam pistol when possible and heat when they're close, swap to the Illegal blade/Photon to clean up. Last set is Kazuya Amon, a few bosses with weapons and 2 gun guys at the back. Spam pistol at Amon when possible but moving and dodging is important. A trick with Amons is that once you've done a heat action with one weapon type, it'll keep doing less damage so swap out with another type of weapon to keep doing decent heat damage. Don't use heat when he's got his orange shield up as it won't do damage but you can still hit him with a photon weapon to knock health down. He'll eventually turn red and into his heat mode, he's dangerous here but also now weak again to heat actions. Swap to the payback ring if you're getting low on health for more damage and make use of extreme heat, you'll never die in extreme heat but you will come out of it with 1hp so be careful you won't leave anyone alive!
Eternal Twilight - 4 sets this time, first is 2 boss ninjas and a bunch of ninjas and samurai, the next waves features 2 coliseum bosses and a bunch of guys, wave 3 has 1 coliseum boss and some more guys. I had great success just spamming my pistol at everything that moved in the first 3 waves, just move around in wave 1. The last wave is only 2 guys with Jiro Amon. It's well worth using a Sacred Wood Armour here since he spams his Uzi at you and it can cause big damage. One tip is if you can actually grab him, you can heat action throw him off the bridge for a quick win. If not, you can use the west side of the bridge to help cover against his ridiculous Uzi spam. Same tips above apply, spam pistol and you can occasionally stun lock him into his shield phase. Photon (but not heat) him in his shield phase and in his heat phase either extreme heat or any weapon spam will do.
Pandemonium - This is absolutely hectic. You'll have to fight 100 guys here! If you're not careful all of Kazuya, Jiro and Sango Amon all at once. First wave is maybe around 50 guys or so with slightly more weapons leading to some with shotguns toward the end. Hit and run works best for this wave. The next wave is around 15 or so guys and Kazuya, he's exactly the same as his mission but take care in only trying to hurt him. Kill too many minions and the next Amon will spawn! It's easier said than done but having three Amons at once is a nightmare. The best strategy I found is to run around the structure in the north, this will buy you some space and time to strike the Amon then run away around the other side of the structure. This will also help when the second Amon drops, as he loves to spam his Uzi. Finally the last Amon drops with his rocket launcher, he works like Jiro so hit and run around the structure works. You can swap out any armour too so you can apply your sacrifice stones if you're getting too low. Having a bunch of different types of weapons really helps here since of Amons ability to take less subsequent damage from heat attacks from a single weapon. Good luck with this one!