Bicycle Mechanics - Chain slipping

Hello,
I have a Rocky Mountain Fusion about 2 years old, and I'm starting to get a problem. When I get into gears 2,8 or 3,8 the chain constently slips a sprocket during hard pedeling. My front derailer is a Shimano Acera and the rear is a Shimano Deora. I'm no expert with bikes eaither, I just like to ride them, so if there is a fix, please try to keep is easy to understand. And thanks.

It's likely that your chain is worn-out (and has thus "stretched") and as such as worn out the sprocket teeth that you use most. In that case, you'll need to replace the rear sprockets, usually as a package (since it's a cheap bike, sprockets don't come separately).
Is sprocket #8 the sprocket you use most often?

I don't know whether "8" is your smallest or largest sprocket on the rear wheel. If it's the smallest sprocket, it's possible to replace it alone.

I'm guessing the chain slipping occurs on the rear wheel (in sprocket #8) rather than the front chainrings (#2 or #3), because
a) rear sprockets nearly always wear out before front chainrings
b) if it's an adjustment issue, rear is usually more finnicky than front
c) #8 (rear) is the common factor in both of your problem cases.

It's also possible that this is a limit-screw issue, where the rear derailer's limit screw is in too far and keeps the derailer from lining up with sprocket #8, while it can line up with the rest of the sprockets.