I found it easier to grab the tank in the base at the top left of the first map. You instantly get a six-star wanted level needed to spawn enemy tanks. You want to not drive too far and instead stay in a small area. If you get too far from the chopper and cops they're prone to lose sight of you and delay tanks from spawning.
When your tank's health is low, either wait until another tank shows up and carjack it or go back and get another from the base. Note that you don't get credit for shooting an empty tank so shooting the tank at the base doesn't count.
You can check progress by pressing
to go to the Statistics tab.
You can also combine this with the Rollin' Rollin' Rollin' achievement where you need to crush 250 cars:
Take the tank across the bridge and to the used car lot. Much easier to crush parked cars than moving cars. Here's a video: