When going through the Most Wanted list from a police computer (LB when in a police vehicle), don't go in order from top to bottom. You can still access the map while browsing each criminal's details and therefore can ascertain which is closest to you. It saves a ton of driving since there's at least two in each list that are in the same area.

You have no time limit for these missions, so make sure you've topped up your health (be it from an ambulance, vending machine or whatever) before attempting each one. It's also a very useful time to call upon Dwayne's special ability, if you've unlocked it.

Remember that there's three Most Wanted lists to go through, one for each borough. That's thirty criminals to hunt down. You have to travel to a different island to view its Most Wanted.

Good luck, Officer Niko!

I have completed 20 so far. Pretty easy, especially if you hide behind a vehicle and pick them off from a distance with a sniper rifle.

Whenever I have to give chase to a criminal(s) I always try to go for the tires first. Popping one or two is very helpful in stopping your target. If I fail in getting good enough tire shots, I'll go for the back window and spray SMG bullets back and forth if there is more than one target in the vehicle.
Ramming your target from the drivers side door is useful as well, as it stuns them for a few seconds, giving you enough time to fill their melon with some lead.

Apart from that most of the criminals are easy enough to just hit with your vehicle to kill them.

quote Jak66

I have completed 20 so far. Pretty easy, especially if you hide behind a vehicle and pick them off from a distance with a sniper rifle.