Heres some tips i tended to use.
1- Explore the levels, destroy all crates.
Getting the Style Point Bonuses really helps out, so keep your eyes open for any nearby crates. Although some of the 1000 points are somewhat out of the way, so explore.
2- Arena mode. Get all the powerups and keep a 5x multiplier.
Dont shut the gates, and kill all the enemies till they stop respawning. (unless you keep getting your ass kicked, in which case shut afew, and focus on the remaining ones.)
3- Chain moves.
A slow-mo jump kill will get you a small amount of points
A slow-mo jump into a dive will get you more
Wallrun-Jump-Dive will get you alot more
And if you use the sword, use the Slide-slash move, or Jump/wallrun slash moves.
These will get you more points
Also headshots give you more points (although, even if it didnt, it should be a rule in shooters, to aim for the head)
Would you kindly?