With your hammer equipped, use it to hit and kill 20 birds cumulatively. The issue is, when your approach a given bird, it will likely fly away unless they get stuck. To make this easier, spend five of your hard-earned upgrade points on upgrading the hammer which will allow you to throw your hammer.
Once you have your upgraded hammer, load the Belfast map (as this map tends to have the most birds) and throw your hammer around so Thor would be proud. Upgrading the hammer will also unlock the following: