Mountain bike, chain skips when force applied from stop or going uphill.
In my experience, chain skip can be caused by various factors, some are easy to fix and some are more difficult. Lets work our way down. 

1: dirty/dry chain. A chain that is not properly cleaned and lubed will cause shifting problem. Get a good chain cleaning tool and de-greaser and clean your chain really well. Then apply a good chain lubricant generously. Afterwards, wipe as much of it off as you can with a dry rag. It is important to use a chain lubricant (not wd-40 or something like it), that is meant to not collect dust. It is also important to wipe off the lube when you are done. You won't be able to get it out of the pivots - which is where it counts. This will fix most shifting problems. 

2: Stretched shifting cable: If you recently had your bike tuned, it is likely that the rear shifting cable was replaced. New cables will stretch. The cable tightness will need to be adjusted after a month or so of riding. Either research how to do this tuning or take it by the bike shop that tuned it - they probably won't even charge you. 

3: Worn chain: Chains wear, and they wear differently based on how they are used and maintained. A worn chain won't engage properly with the teethe of the cassette and will cause major shifting problems. If you are serious about maintaining your bike, you will need a chain checker. I personally like this one (https://www.amazon.com/gp/product/B001AYMR7Y/ref=oh_aui_search_detailpage?ie=UTF8&amp;psc=1)

4: Worn cassette: If you change your chain on time, a cassette will generally last in the order of 3-5x chain changes - but eventually it will need replaced. There are plenty of resources to help with that (http://www.artscyclery.com/learningcenter/determiningcassettewear.html)

5: Old cables: Shifting cables and/or housing that are old and potentially frayed or rusted will cause shifting problems. Likely, though, this will have been addressed during your tune-up. You might want to verify though. 

6: Other: Those mentioned above are the most likely culprits. However, there are other reasons that are more advanced to troubleshoot. These include, but are not limited to; a bent dérailleur, poor shifting adjustment, a cassette not properly tightened and a bad a bad chain link.

I suspect that if you address items 1-3 in order you will find that your problem goes away.