This is guaranteed way of getting this achievement, and the other two points achievements along the way, in less than five minutes.
Use two controllers, start Original Mode, and press the bumper buttons on both controllers to add credits to the game.
For P1, choose Charlotte. For P2, any character will do. Once the game starts, press up on
, and as you're dropping down, press
. If done correctly, you'll do a downwards heavy slash attack that takes a chunk of health off P2. Repeat till you win, and repeat for the Round 2. You should now have over 100,000 points. Do not continue on P2. Instead, once the next round starts, press
, and choose to "Create an interrupt save".
Leave the game, and go to the main menu. Choose Original Mode again, and the game would load from where you created the save. The 100,000 points achievement should automatically unlock now.
Press
on the second controller now to join the game as P2, and repeat the above until you get 200,000 points. Do not continue on P2, create an interrupt save, leave the game, and return to unlock the 200,000 points achievement.
Press
on the second controller again to join the game as P2, and repeat the above until you get 300,000 points. Do not continue on P2, create an interrupt save, leave the game, and return to unlock the 300,000 points achievement.
The reason you need to keep leaving the game is because the achievements do not unlock when you're doing versus matches, even after you finish them without continuing on P2. By using the interrupt saves after you hit the landmark scores, you're basically tricking the game into thinking that you've gotten those scores solo. You need to do it for each landmark score because if you go straight to 300,000 points, the two lower scores achievements won't unlock.
Hope this helps!
PS: You can use any character you want for P1, but Charlotte's cheap move ends the fights very quickly, and give you maximum points in the least amount of time.