I will show you two methods to free up app's space. I personally like Method 2 more because, it gives more freedom in choosing what to delete and what not to.
Method 1: Clear cached Data
- Go to Settings > Storage > Clear cached data (for all)
Method 2: Using Storage Analyzer & Disk Usage app (Requires Android 4.1 or up)
- If you can't install anything from the start, I suggest to first uninstall apps that doesn't necessarily contain essential app data--one that you don't mind losing data for when you uninstall it, e.g., Facebook and Messenger apps (uninstalling any of them is actually enough). The app is only about 4 MB in size.
- Install Storage Analyzer & Disk Usage app
- Open the app called Drives (this is the app's name in my phone).
- Wait for it to finish its scanning.
- Go to the DEVICE'S STORAGES tab.
- Click Applications, then wait for it to finish it’s scan.
- Go to FILE CATEGORIES tab and delete all deletable stuffs except stuffs of the same type of App data.
- App cache is usually what you want to delete.
- App apk is usually undeletable, but it's just all the app apks you downloaded from the first time you got the cellphone, so it would be good if you are able to delete this. (As an aside, you can also comment to this answer how will I be able to do that).
- I repeat, DO NOT DELETE App data or other folders of the same type because they're your app data.
- Note: If you are able to delete a folder or a file, that file will be immediately deleted, no questions asked. So be careful.
- Reinstall the apps you installed in the first step.