You need to know how to drive for one thing. If you're hitting everything and have a boat for a car you're not going to be too well off.
Second would be you need a good car. Some cars are better at running through blocks (such as heavier or AWD cars), whereas some are just so fast you can actually outpace even the fastest level 5 cars (although you really need to know how to drive, maintaining 190+ on the highways)
As far as the pursuit breakers, you need to make sure that the cops are RIGHT on your tail when you hit them, otherwise they'll just drive around the mess you created and keep coming after you.
As was mentioned before, stick to the highways until you've accomplished your goal, then you can dip into the city to hit some pursuit breakers or lose them around corners and dive into a hiding spot or safe house.
Another trick is to just sit when you've finally ducked out of sight. You can often sit on something like an exit ramp or back alley until you cool off instead of risking a sprint to a hiding spot or safe house where there might be cop cars along the way to reengage you. Obviously it takes longer to cool down but I've successfully done it more often than not.
The last trick would be to find an area such as the bus station where you can smash into it and drive up the ramps, sitting up there until you've "lost" the cops. Granted several times I've done this the cops were right in the bus station with me but are too dumb to make it up the ramp. Sometimes you need to drive around up there so you keep out of their line of sight. Once thats done you can just jump to your safehouse and you're safe. There are other areas just like this, you just have to find them.