Viva LA Barkers, guide is good, but to just to give a little more detail, there are 7 frames in the snooker element, then 3 frames of 8 ball and then 3 frames of 9 ball pool.
You need to win at least 7 of the 13 frames across all games to get to the next round.
With that in mind, and depending how many stat points and general experience you have when taking this on, I personally often found it quicker to do my best in the snooker, but if I lost 5-2, that was ok, as I knew I could make it back in the pool elements.
During this game mode I found that for me, If i used the quit to dashboard trick during the snooker, when I restarted the match the scores were reset to 0-0 frames,which is why I tried to avoid doing it.
As i didn;t have many stat points when doing it, for me it was quicker to just get thru the snooker, then do well in the pool, as the pool matches are far quicker, if I needed to quit to dashboard on those, it wasn't a big a deal to replay 3 frames.
If you are playing this and do really well in the snooker and win all 7 frames, you could conceed the pool matches at your first opportunity to speed things up and get thru to the next round quicker.
****EDIT***** Please see this extra info I missed when writing the guide, Thanks to Skadi And Omega for pointing it out
"when you get to the final, you MUST win the final pool match (8-ball) for it to count as a win, regardless of how many frames of snooker/pool you have won up to that point. Failure to win the last pool match will result in your opponent being awarded the win.
Posted by Skadi And Omega on 25 Jul 11 14:26:17"