OK I've been in this situation many times, playing 8 ball on a bar box against someone much superior. I have a few tricks and strategies for dealing with such opponents. Actually, a few days ago I played a guy who had two times my accuracy, ten times my position play and three times my planning capabilities. I stuck to my strategy and won.
The problem is, I play by regional bar rules, so my tactics aren't compatible with WPA or BCA rules. The good thing is that you said you play in APA, so I guess you use APA rules, which is just fine. Here are a few tips which should help you improve your win/loss ratio against players with greater skill:
1. Always choose the balls which block your opponent's balls in the start. For example, if stripes are mostly positioned between the solids and most pockets, preventing the opponent from scoring anything during the first few shots, go with them.
2. Be patient. Don't go for low-percentage shots. If your opponent is highly skilled, let him do that. Eventually he'll miss, allowing you to punish him by pocketing some easy balls.
3. If you don't have a good shot, you have two options:
a) Play defensively. Simply hide the CB on a difficult position and let your opponent play. If he does the same thing, be persistent and keep repeating the same defensive move until he freaks out, shoots and most likely misses. Remember: nerves win this.
b) Use "heavy artillery" someone else mentioned before. It's not a recipe for disaster if you use it at the right moment. Some situations require you to forget about planning ahead, aim for the largest cluster of your balls and blast away with full power. Just make sure you don't accidentally pocket the 8 ball. This option is a risky one and requires a lot of thinking and practise, but it usually turned the tide of the match for me.
4. Go for easy balls, but leave the ones positioned near the pockets right where they are. With them guarding the pockets, your opponent will be forced to drop them first before pocketing his own balls, or at least waste a shot to kick them out of the path.
5. If he pockets most of his balls while you pocketed almost nothing, use this to your advantage. Play defensively and keep hiding that white around. At the same time, you have an open table, allowing you to go for easy balls.
6. If you pocket the majority of your balls before him, he'll most likely catch up. He'll also keep blocking your every shot. That's where artillery comes into play again. If he hides the white behind a cluster of his balls, blast away (off the cushion if necessary) in the direction of your remaining balls. You don't really have much to lose, but there's a lot you can gain. Just make sure you actually hit your balls
There's much more I could say about this topic, so pm me if you're interested, but for now you should do fine with this along with the great advice from other posters.