Notice: This method is undocumented and only for tweaks or apps that will not be submitted to AppStore.

How to use:

[[UIApplication sharedApplication] setSystemVolumeHUDEnabled:NO forAudioCategory:@"CATEGORY_HERE"]; // for a specific audio category

OR

[[UIApplication sharedApplication] setSystemVolumeHUDEnabled:NO];

Relevant header (private methods):

@interface UIApplication (Private)

- (void)setSystemVolumeHUDEnabled:(BOOL)enabled forAudioCategory:(NSString *)category;
- (void)setSystemVolumeHUDEnabled:(BOOL)enabled;

@end

Reference: List of available audio categories