Manual Method 2 (For OSX or otherwise)
If you're having trouble unzipping the files, never fear -- there's a tool that will do that for you.
1. First what you'll need to do is download the various updates that you'd like to apply. Again, you can get those here: http://www.arcengames.com/dl/AIWarBetaUpdates2.xml
2. Normally you would just unzip those, in order, into your AI War folder. But if that's giving you trouble (such as on OSX), then instead take the files and put them inside the RuntimeData/updates folder in your AI War installation directory.
3. Rename the files to just VersionNumber.zip. So for instance if you download version 4.032, with a filename of AIWar4032.zip, you need to rename it to 4032.zip in the updates folder.
4. Once all the files are in place, create a new plaintext document called "updatelist.txt" in that same RuntimeData/updates folder.
5. Inside this document, put the version numbers all on one line, separated by a single space between each version. Put these in the order that they should be applied, so ascending order. In other words, the same order you'd put them in when unzipping them by hand. An example document might look like this, with a single line saying: "4032 4033 4044" to apply 4.032, then 4.033, then 4.044, for instance.
6. Once both updatelist.txt and the actual zip files themselves are in place, go back to your main directory for AI War and run AIWarAutoUpdater-windows.exe or AIWarAutoUpdater-osx.app, depending on which platform you are on. The auto-updater does NOT download anything, it simply unzips the files you have already downloaded based on the updatelist.txt file. Normally the game itself does the downloads and creates the updatelist.txt file, but if you do it by hand the autoupdater can't tell the difference (so long as you do it right), and will save you the trouble of unzipping if that's being problematic. For most people, unzipping by hand is faster, though.