Zombiewood is a dual-stick shooter released by Gameloft a little while ago, and while the dual-stick shooter is probably one of the most iterated forms on the App Store, there's enough style and polish here to give the game a look. It's available for free now, so there's not much to lose anyway.
The core idea of the game is that you're an action star shooting zombie movies around various Hollywood locales, but of course that's just an excuse to throw the player in a variety of locations, along with a gun, infinite ammo and a horde of angry zombies. Each level has a series of different goals, from just killing all zombies to time limits or special collectibles, which provides a lot of replayability from session to session. And there are quite a few different weapons to buy, and coin to collect for various cosmetic or power upgrades.
The game is definitely a freemium title, and if you want the really good guns, you'll probably have to put some real cash in. But I didn't find that was necessary -- even the guns you buy with in-game currency can be pretty powerful, and there's enough fun in just trying to unlock every level's goal to keep you playing for a while. Plus, the game is well-done, with a kooky and colorful art style, and the controls are well-tuned. You can see the whole thing in action below -- as a free-to-play dual stick shooter, Zombiewood won't disappoint.