To get the These Dreams achievement in State of Decay 2 do the following:
Plague hearts are one of the big new additions to this sequel. You'll be taught how to find and destroy them in the early hours of the game, unavoidably. Then you'll just need to find and destroy four more. You can use Influence to ask survivors to locate more plague hearts or you may just happen upon them while out in the world.
The game suggests that you bring explosives and loaded firearms to most efficiently destroy the plague hearts. My additional crucial tip would be to bring decoy items as well, like fireworks and radios. After every few blows to the plague heart, another wave of zombies will come and they'll be the more difficult kind that can infect you if you take too much damage from them. Use decoys and your environment -- ladders and climbable cars -- to keep your distance and take them out with relative ease.