Well I have tried to run away from helicopters like a hundred times and I have reached the objective only once, I do not really know what I did but I started driving all around the city and started to switch between cars, mover from a city to another and stuff like that, I do not really know what I exactly did but you should try doing what I did and see if it works or not, however you could always try to hide underneath bridges and so on.
Hiding under bridges is good, up until they start hovering around at the entrances and spot you again. I did this a few times, even with a helicopter under one of those natural coastal archways, but every time the police helicopter starts to hover around the entrance and you're spotted again.
Is is my favorite option as well although I only ever do it if I'm just having fun and not trying to finish any specific missions because I know if I do this it will just increase my heat level.Shoot it down! It's literally a mosquito.