I've had this mountain bike a little over 2 yrs. I had it serviced when I bought it because it was recommended even though it's not an expensive bike. One day the chain slipped off multiple times which had never happened. Once I flipped it over I noticed the cassette was wobbly. Would this be an expensive repair and what exactly should I be looking at to have replaced?
Could be a number of things:
Cassette is loose on the freehub body. If the cassette lockring has come loose the cassette sprockets can slide axially on the freehub body and possible 'rock' on it a little. If you take the wheel out of the frame you should be able to see of the lockring is loose quite easily. To tighten it you need a chainwhip, lockring tool and a big wrench. It would not cost much to have local bike repair shop do this.
Freehub body is loose on the hub: If it looks like the cassette is firmly on the freehub body, but is moving relative to the rest of the hub, the body may be loose, or one of the bearings supporting it is damaged. To tighten the freehub you'd need to get the cassette off, and then figure out how your particular freehub is secured. Again, your local bie repair shop can do this for you.
Possibly the axle or hub bearings are broken. With the wheel in the bike try pushing and pulling laterally on the wheel rim. If there damage to the bearings there will be movement.
If the freehub or hub bearings are damaged on an inexpensive bike the best thing to do is just get a whole new wheel. Inexpensive wheels are not worth rebuilding to replace the hub as the cost of rebuilding will be a significant fraction of the cost of a new wheel.