From your starting point as a plant head left to the RV with a Town Centre sign in front of it. Once you arrive head straight for the sun flower (Major Sweetie) found within the barn and he will give you a mission that results in you obtaining a lawn mower. (If you have this done skip the next paragraph.)
Head east and free 2 plants that have been imprisoned within forcefields for a little backup. You will then find the road blocked and have to head underground and be denied passage. Once you head back above ground you will have to free the lawn mower from another forcefield. Then defend it while following its twisting path to deliver it to the Major. Ask for your next assignment.
Major Sweetie will ask you to find 3 items to disguise the mower as a zombie. The nearest exclamation point will lead you too a Cob that will point you to another sewer and you will find Baron Von Bats. After a battle with him he will curse you and leave you to be cured by a device with a short radius. You will be in combat with minor zombies the entire time.
You will then have to track down Von Bats and fight him while he travels with a moving musical caravan and constantly battle against minor zombies along the way. Cursed once again you will have to find and turn on (by holding X) another device.
You will then have to travel to Von Vats' concert and complete your final showdown with the Baron. Lots of teleporting and minor zombies to fight in this battle. Once you defeat him you will get his Hat and the achievement will unlock.
I used the snap dragon myself during all this. Make sure you stop to let yourself fully heal whenever the opportunity presents itself. I also had upgrades to boost my health with vanquish and my standard movement speed (these have to be chosen while you select your plant).
Good luck! Please let me know if I need to add anything. Thank you for reading.