I did some checking and it doesn't seem that Apple provide a way to check disk space when using ALAssetLibrary. They do however provide an error code, it the operation failed due to disk space issue.
I suggest you just try save the image and make sure you check the error returned in the completion block and notify the user accordingly.
ALAssetsLibraryWriteImageCompletionBlock has a NSError argument which can be one of the following
Error Codes
AssetsLibrary-related error codes
enum {
ALAssetsLibraryUnknownError = -1,
ALAssetsLibraryWriteFailedError = -3300,
ALAssetsLibraryWriteBusyError = -3301,
ALAssetsLibraryWriteInvalidDataError = -3302,
ALAssetsLibraryWriteIncompatibleDataError = -3303,
ALAssetsLibraryWriteDataEncodingError = -3304,
ALAssetsLibraryWriteDiskSpaceError = -3305,
ALAssetsLibraryDataUnavailableError = -3310,
ALAssetsLibraryAccessUserDeniedError = -3311,
ALAssetsLibraryAccessGloballyDeniedError = -3312,
};
If you want some additional checks before, you can use the method mentioned in the comments to find the available disk space on the device, but there's no guarantee AssetLibrary doesn't use different logic to calculate disk space requirements.