Well, I just finished my first playthrough of the game on hard.(Had 63 000 at the end of Chapter 8)
Got a total of 89 350 points.(all upgrades + 23 350)
So if it can help anyone that's how I did:
-Use pistol all the time
-Upgrade special moves and 1 of health
-Upgrade to the max pistol rate of fire and one of damage
-Upgrade every moves then buy everything else but pistol damages until the end Then buy it.
My guess is, since pistol did almost no damage, I had to do head shot to get kills, and points with it.
I kept trying to use moves that gave me the most points (Wall jump mostly) even if it only worked 10% of the time
Completed Arena at 100% like it is pointed on the guide.
And I'm not a pro of shooting games, so someone good would probably reach 100 000.