You can do it, but it's a lot of work.
Soundproofing is a well defined science - the folks that build recording studios have it all figured out. I was designing a home studio for my previous house so I did a bunch of research and read a couple books. I'm far from an expert but I did learn a lot. There are some good books and web forums out there - I'm travelling now so I don't have It gets pretty complicated but the main ideas are:
Make sure there are no direct air paths between the spaces to be separated. If there are air vents, leaks, etc between the attic apartment and your garage, you need to get rid of them. If there is necessary duct work, there are solutions (mostly buildign labryinth type devices)
Since it's likely much of the sound is being transmitted between the garage and the apartment above is through the ceiling, you can help some of that by insulating and isolating. Insulate the space between the garage ceiling and the apartment floor. The type of insulation matters - Rockwool is the preferred type for this sort of thing. It's not cheap and will be hard (impossible?) to install if the ceiling is already drywalled.
Assuming the garage ceiling is already drywalled, you can isolate by adding another layer of drywall to the ceiling and using "isolation" channel. There are a number of types:
"Resiliant Channel is popular:
http://www.markertek.com/Acoustic-M...truction-Products/Auralex-Acoustics/RC8.xhtml
Another more complicated system:
http://www.soundproofingcompany.com...s/furring-channel-with-resilient-sound-clips/
You're basically putting a spring between the new drywall and the existing drywall. The idea is to create a membrane that's not rigidly connected to the existing ceiling. You screw the channel to the existing ceiling and then screw the new drywall to the channel. The channel is thin and flexes which is exactly the point. Also, the new drywall cannot touch at the walls so you need to leave an 1/8" gap all around the edges. You need to fill the gap with special "acoustic" caulk to seal it against the walls (no air leaks allowed). The acoustic caulk remains flexible. The idea here is that the "membrane" drywall layer will absorb the sound by moving, reducing the amount of energy in the sound pressure waves so not as much energy is transmitted into the floor above. You might need to do this to the walls, too since some sound could be transmitted via the walls into the ceiling/floor above. That's probably getting into waaaay more than you want to do!
There is a ton of good information out there on the web. Here's a good forum:
http://www.johnlsayers.com/phpBB2/index.php Lots of good info, quite a few experienced people that are willing to help.
Here's a place where you can learn some of the basic about the mechanics of sound transmisstion and isolation:
http://www.acoustics101.com/ Chapter 3 has some info about ceilings.
Hope that helps!