ANARCHY REIGNS

Stage 3 consists of 6 missions, but only the Story Missions are required for this achievement. Once all 3 story missions have been cleared (regardless of rank), a cutscene plays and the achievement pops. Missions are unlocked based on points, so if you encounter a Free Mission that proves to be too difficult, you can continue grinding another Free Mission or you can continue fighting in the streets (non-mission mode).

The 6 missions:
3,000 points - Break It Up - Free Mission - In this mission, you're supposed to kill 50 drones in 5 minutes. I absolutely could not complete this mission on this difficulty, so I skipped it and spent time in street brawl grinding points to unlock the next mission.

100,000 points - Night Blooms - Story Mission - Boss fight with Rin Rin. This boss is very fast, so you'll need to dodge her attacks and then combo her when she's open. At 3 points during the fight, the stage will go dark and she will teleport around and throw a flaming sword at you. The easiest way to deal with this is to just back away to the other side of the platform because the sword throw has very limited range. Since you can't hurt her during this phase, just wait it out and when she comes running at you, resume the dodge/combo routine until she's defeated.

300,000 points - Cleaning Up Hong Long - Free Mission - This is the mission I used for grinding the rest of the points required to unlock the other missions in this stage. You have a 5 minute timer and need to push 10 balls into their goals while avoiding a few enemies that rarely bother to even take a swing at you. I was easily earning 120,000 points in just over 3 minutes here.

500,000 points - Enter the Ninja - Story Mission - Boss fight - This guy has been playing way too much Ninja Gaiden and will quickly combo you to death with his Ultimate Technique if you're not careful. Luckily, you have 2 AI teammates here, so hang back and let them do the fighting when you can and sneak in for a quick combo when you see a chance. At 3 points in the fight, he will summon drones to assist him and teleport to the center of the arena to use Ninpo attacks. The easiest way to survive these phases is to just run around and continuously grab the drones until they're all dead. Once you've cleared out all of the drones, carefully combo the boss. I never successfully managed to grab this boss, but I got my face kicked in when I tried, so I would recommend avoiding it. This area also has 3 large columns surrounded by electricity that will hurt you if you get near them. If your AI partners go down, walk over to them and they'll get back up with full life and keep fighting.

600,000 points - Bartender Backup - Free Mission - I read the description on a GameFAQs walkthrough that indicated that this mission has 10 bartender bots running around and you have to keep them alive. That sounded annoying to do on hard, so I skipped it and just did the previous Free Mission again.

700,000 points - The Wounded Beasts - Story Mission - Boss Fight - Again you have 2 AI teammates in this fight, but with no additional support being summoned to assist the boss, this fight is actually VERY easy. I let the AI teammates pound on him and repeatedly got in behind him for grabs. When things started looking bad for me, I just backed off and let the AI teammates do the work. If they go down, you can get them up again by simply walking near them and they'll resume fighting with another full life bar.

*Need to double-check points requirements.