I figured I would give some pointers on how I went about knocking this one out (pun intended). It's important to remember that, when it comes to Peggle, there's more than one way to skin a cat, so I'm sure there will be lots of useful strategies that won't be listed here. Feel free to let me know in the comments, so I can add them to the solution! Remember, Peggle is 20% skill, 20% luck, and 60% teeth-grinding persistence (but I'm sure you already know that). Anyway, here are a few strategies that I found useful...
Gnorman is your best friend. I found that Gnorman was, by far, the most useful Peggle master. I used him to complete a vast majority of the objectives. There are a few cases where the other masters are more useful (generally in the levels associated with them during the "story"), but I highly suggest using Gnorman as much as possible. Believe it or not, I found many of the "Ace" objectives to be far more taxing than the "Clear All Pegs" objectives (your mileage may vary). That being said, I was able to achieve nearly every "Ace" objective with Gnorman.
Don't be afraid to repeatedly restart a level before jumping in. Every time you restart a level, the location of the orange and green pegs change randomly. Sometimes I would spend a solid minute hitting restart over and over until I got the green/orange peg setup that I considered most optimal for a given level. Maybe you need a green peg near the top, maybe you need it near the bottom, or maybe you need the orange pegs a little more condensed. In any case, don't hesitate to keep restarting until you get the setup you're looking for.
Don't waste time on a mediocre run. If you're 3-4 shots into a level, you've already used a green peg or two, and you feel that the run is decent at best, just restart it. This is especially true when dealing with the "Clear All Pegs" objectives. By the time you have used both green pegs, you should feel like you are doing EXCEPTIONALLY well. If you don't feel fantastic at that point, you're probably better off restarting. Just remember, more time is wasted on bad runs that you play out than runs that you restart early.
Leave a single orange peg as high as you can to hit last. This pointer is only for to the "Clear All Pegs" objective. Sometimes when you're clearing all the pegs, you accidentally hit the last orange peg, effectively ending the level. This is enraging. I can't tell you how many times I have had PLENTY of balls left, only a few pegs left to go, and accidentally bumped the last orange peg to end the level. If you leave yourself an orange peg near the top of the screen, you eliminate the chance of accidentally bumping it while clearing.
Practice your "Free Ball Skillz." The "Free Ball Skillz" skill shot is when you bounce the ball directly off one peg straight into the bucket. I honestly cannot say enough about this. I saved it for last, because it is seriously the single most important aspect of the "Clear All Pegs" objectives. I would routinely have runs where I had 2-3 balls left and 10-20 pegs remaining. I would just hit each peg, one at a time, bouncing the ball straight into the bucket. I have a few additional pointers for this.
Firstly, always try to take care of the lower and middle (vertically) pegs in the level right out of the gate (before starting your "Free Ball Skillz" spree). The reason for taking out the lower pegs is because your targeting line only extends so far. It's MUCH easier to aim your shot when you can hold your targeter flush against a peg. The reason for taking out the middle pegs is because you want as much room as possible when lining up your shots. You'll see why here in a minute.
Rectangular pegs are, by far, the easiest to do. When aiming at a rectangular peg on the right side of the screen, put your targeter directly against its left side (the opposite when aiming at a peg on the left side of the screen). Because the sides are flat (obviously) the margin for error is gigantic. Just wait for the bucket to pass below, and slightly to the left, and fire. After a couple of these shots, I can promise you that you will catch on quickly.
Circular pegs are more difficult. For these, you always want to bounce the ball across the screen in the biggest arc possible. What I mean by this is if a peg is on the left portion of the screen, you want to bounce it such that the resulting arc makes a rainbow all the way across to the other side and (hopefully) into the bucket when it's directly against the wall. The reason why I prefer this method is that it increases your margin for error significantly. This is due to the fact that, if you over shoot your target (the bucket), it will bounce off the wall and straight in anyway. As such, when aiming your shot, always err on the side of too far, since you have the wall as a buffer. Using this strategy, I am able to make a solid 90-95% of the shots. This is a big deal when you have a bunch of pegs to take out and only a few balls to do it with.
Lastly, note that when you hit 5 of these skill shots in a row, you will get the "Mad Skillz" skill shot, which is worth 25,000 points. Furthermore, if you hit 10 of these in a row, you will get the "Crazy Mad Skillz" skill shot which is worth 100,000 points! This is super useful when trying to get those "Ace" scores on certain levels.
There really isn't a hard and fast way to get this achievement. As I said before, persistence is the key (along with lots of "Free Ball Skillz" practice). I realize that many of you may be stuck on a very specific objective/trial; as such, these generalized pointers might not be very helpful to you. If this is the case, tell me what objective/trial is ailing you, and I will try my very best to give you any additional help I can on that level. I will attach any such help directly to this solution.
If you guys have any other questions or comments at all, please say so in the comments section! I will be happy to assist in any way I can!
Good luck! :-)