you need to figure out if you have a freewheel or a cassette. those are two totally different things that do the same thing. look that up. based on the data I can find, it looks like the 2010 Aggressor has a 7-speed freewheel.
if your freewheel "wobbles" that is common and there's not much you can do about it. I doubt it's causing any problems unless somethings is severely damaged by a big impact.
There are a lot of moving parts on a shifting drivetrain that might need attention. from the top down:
- shifters need to operate smoothly. if they are sluggish and don't engage and stay in the right gear, you might need to open them up and flush them out to get them moving again.
- cables need to be as friction-free as possible. if the plastic lining inside the shift housing is worn or gummed up, the shifting will suffer. if the housing ends were not cut and capped correctly, shifting will suffer. if the cables themselves are corroded (or worse, rusty) or fraying under tension, shifting will decline.
- derailers need to be adjusted. cable tension, alignment, limit screws, etc. need to be set just right. the rear derailer hanger must be aligned, and one of the most common causes of poor shifting is a hanger that is bent from being knocked when the bike fell over or crashed.
- cogs and chainring teeth need to be in good shape. they wear out with time and miles.
- the chain needs to move freely and smoothly. chains also wear out with wear, usually long before the cog and ring teeth wear out.
books have literally been written on this topic. you're have to take some time to familiarize yourself with basic terms and functions of your bike or all of the suggestions you get on this forum will sound like gibberish to you. spend some time with Sheldon Brown's website and Park Tool videos to start.