This ones the second toughest achievement in the game (not including DLC, I havent adventured there yet so i would'nt know). Theres a long list of challenges for you to clear, but I think I can help you get through a few of the more difficult ones. The challenges don't have to be done in any specific order, so don't worry about getting them done any certain way. If for any reason you're not getting past a certain level, leave me a comment, send me a message, or message me over xbox live. I'll try and help you as much as i can.
1-1 Through 1-5
These are pretty simple. Clear all of the orange pegs in the level. The catch is that these levels have 35 orange pegs as opposed to the 25 you normally have. I would suggest using Tula (the sunflower) for her ability to clear out 1/5 of the pegs with one green peg. For level 1-5, use Claude (the crab) and make sure you hit a green peg with your first shot. You can keep the ball up and clear almost the whole top half of the level. This tactic will come in handy later.
2-1 Through 2-5
Same concept as the last set of levels, except theres 45 pegs instead of 35. Use Tula to clear the level as quickly and efficiently as you can. It might get tricky, but its not hard, i promise.
3-1 Through 3-5
Adding on ten more orange pegs to clear. Clear 55 orange pegs per level. Again, Tula will help you the most, and its not difficult.
4-1 Through 6-5
4-1 through 4-5 is simple, score 300,000 points per level. 5-1 through 5-5 and 6-1 through 6-5 are also score challenges of 350,000 per level, and 400,000 per level. 300,000 is right around what I'm assuming most people score on average per game. However, if you have trouble scoring that high on certain levels or you cant reach the 400,000, there are a few things you can do to help.
-Before you jump into challenge mode, keep in mind that you can get these challenges completed in quickplay. This benefits you because if you happen to clear the level in quickplay while getting enough points to get the challenge done, youre killing two birds with one stone. One step closer to having them all cleared, and another achievement unlocked. Note that if you clear them in quickplay while offline, it will not count toward the challenge levels. I can confirm this from a personal test run of the theory.
-Look at the layout of the level. If it seems to bring your ball to the center of the field (such as the one that says "FEVER") then stay away from: Renfield (the pumpkin), Jimmy (the gopher?), or Claude. Those characters will most likely bring the ball back to the center (where the pegs are already cleared) or do nothing.
-Clear as many orange pegs as you can while still leaving a few (near the top) that you wont accidentally clear.
-Try and have as many blue pegs remaining as you possibly can while having only a couple orange pegs remaining.
- If you have a 10x multiplier, clearing a purple and 4 blues will earn you a free ball, 25,000 points, and get you closer to clearing the stage (This is the reasoning behind the previous tip).
-Try using Warren (the rabbit) in hopes of the magic hat, or triple score ability. You cant go wrong with Hu (the owl. OWL!) because zen shots usually do pretty well. Renfield is also very helpful in some levels as you can get up to 4 free balls fairly easily.
7-1 Through 8-5
This is where it starts getting tough. Clear all of these ten levels. Just like the last three sets, these count if done in quickplay. I reccommend doing them in quickplay because if theyre done in challenge mode, they dont count toward the "Doctor of the Peggle Arts" achievement.
It take patience and time but youll get it. If you get a clump of pegs surrounding a green peg, then use Splork (The alien!!!) and his space blast. Its more helpful than you would think.
9-1 Through 11-5
These are all duels, getting progressively harder. Hu is your best bet for these levels. It's to your advantage to be the one to hit the last orange peg. That was how I cleared most of them.
12-1 Through 12-5
Clear X+1 number of levels where X is the number after "12-". I hate math, but its as simple as these levels. It's easy enough. It's honestly a matter of luck. Getting six good levels in a row is'nt easy, but its definitely doable...and 10 levels in a row is a lot worse.
13-1 Through 13-5
Another set of duels. The only thing is that this time the levels are random and you have to beat the computers total score from 3 levels. Each level is progressively harder but they all only have 3 stages.
-If you have the patience, these can be cleared with no problems at all.
-Keep resetting the challenge until you get "Pearl Clam" as the first stage.
-Choose Claude as your character and hit a green peg with your first shot. Use the flippers to clear as much of the top half as you can. I've scored over 200,000 off of that first shot alone. It's hard for the computer to catch up to that unless you mess up big time along the way.
14-1 Through 14-5
Points challenges! 750,000 to 1,000,000 points. You have 3 levels to earn these. The levels are pre-set so you cant use the trick from the last set. Renfield, Warren, and Hu are a big help. See the "4-1 Through 6-5" section for score boosting tips.
Clear this stage with only two balls?!?!? It's not as bad as you would think. Right before writing this I went back and replayed it to make sure i had the best possible way to do it. Keep resetting it until theres a green peg fairly close to the top of the screen. Use Renfield and hit the green peg. I ended up hitting both on my first shot. On the second shot I had 200,000+ points, 5 more shots, and only 9 orange pegs remaining.
Clear this level with ONE BALL?!?!?! Ok, I just attemped it and cleared it with Renfield. The first time I did it, I used Hu. You have to hit a green peg with this shot and then hope to get another ball. Once you do that, you're almost done. Try and make the ball follow the slope if you can, it helps a lot.
The ten ball trial. I had a lot of trouble with this one. My advice would be to complete 15-2 before this one because you're going to end up with only one or two balls by the time you get to the last level and what do you know, it's the same as 15-2! Remember that you only have to clear these, so don't worry about points.
-First level! Look where the green pegs are located. This will help you determine your character. If they're close to the top (like first or second row close), then choose multi-ball and see how it works out. I used that when i completed it and I got a lot of extra points. If its not working for you, then use Renfield or Hu. Use as few balls as you can (obviously).
-Second level! Use the same tactic. I reccommend Hu for this level.
-Third level. You should have 1-3 balls left for this level. I reached it once with 4, but I was lucky. If you cleared this level with one ball in the 15-2 challenge, use the same tactic you did before. If you did'nt clear that level, check the "15-2" section for tips.
Score 750,000 points. In a single level. Without crying. It's the hardest challenge there is. The trick is to do this is the level "Beyond Reason". You have to be Hu. Clear as many pegs off of the side as possible, leaving one green peg on one side or on the helix somewhere where you wont hit it. On the other side clear a hold in the bottom of the helix two or three pegs wide. Hit the green peg and bounce the ball off the bottom of the bucket or the wall and into the helix. It's difficult, but it's the easiest way (or so i've heard). The zen shot is what makes it a lot easier. All I have to say about that one is good luck.
---EDIT: This was one of the couple levels i had remaining when i wrote the guide. I cleared it right after finishing. I found that Splork is the most useful in this challenge. Ive tried every other way multiple times, but none of them worked. Choose Splork and make sure you have both green pegs in the helix. You want them to be surrounded by orange pegs, but not too close to each other. Start clearing orange pegs off of the side. As soon as you can, hit one of the green pegs to set off a space blast. Try to aim at one near the purple peg. This will give you a pretty big score, ive never gotten less than 200,000. Before you hit the next one, look at your multiplier. If its close the the next one up (mine was at 3x and i knocked it up to 5x with one shot) level it up before hitting the next green peg. On my first shot i got about 200,000, and on my second i got 450,000. I only had a few remaining orange pegs left and less than 100,000 points to get. I ended up with 810,000 after the bonus for extra balls and the fever score. It took me 3 tries after I realized it would be a good combo.
The last level. "The Decathlon". You have to beat 10 random levels in a row. Simple enough, right? Nah. Actually its pretty tough. It's just like the levels in the 12th set. Its honestly just luck. You have to get 10 good levels in a row. With a good setup. Use what you've learned while playing to help you decide on a character, and how to go about clearing the levels. Theres not too much I can say about this one. It'll come to you eventually if you're pretty good at the game.