It is sometimes possible to shoot chickens to continue your combo to the next screen.
To defeat a swag goon without removing his shield use sniper rifle and go for a headshot. For most with shield use this tactic.
You can get a bonus if you shoot an enemy when the warning reticule is on him and before he's launched his projectile.
Tap restart instead of respawn to take you back to the start of the level to try again to get that top score.