Try to learn the best attacks for certain enemies. What I have found most effective is use the
combo on any enemy that you can grab. The bigger enemies are very easily killed with the Splatter Smash combo twice in a row. For the annoying, quick enemies that run away from you, get a weapon like the 2x4 or the metal pipe or the baseball bat and use the basic ram attack on them, it'll kill them in 1 hit.
Using these techniques I have easily been able to get under the time limits on the challenges.