This achievement is fairly simple. Halfway through the first world (Peggle Institute) you will be introduced to trials. Then you will unlock the remainder of the Peggle Institute trials upon completing the last regular level of the Peggle Institute. The trials aren't too difficult, but I've described strategies and methods below:
Trial 1: Long and Long: Get 2 Long ShotsUse the Super Guide to bounce your shot from a peg on the left side to a peg on the right side. Do this a second time to complete the challenge.
Trial 2: The Skillz: Get 3 Free Ball Skillz Style ShotsUse the Super Guide to get Free Ball Skillz style shots. This is when your shot only hits one peg and then goes into the bucket. Time your shots for when the bucket is on the sides of the stage for the easiest timing.
Trial 3: Duo-Slide: Get 2 Extreme SlidesUse the Super Guide to bounce off the circular peg and slide neatly along the rectangular pegs. The Super Guide will get a fire effect if you are lined up for a slide. You do not have to land in the bucket.
Trial 4: Ridiculoso: Clear All PegsSlide your shot along the bottom of the highest ring. Your shot should clear all the pegs.
Trial 5: Big Skillz: Get 3 Free Ball Skillz Style ShotsThis is the same as trial 2 except you don't have the super guide to assist you. For your first shot, don't move and use the background to assist in aiming, then just time your shot correctly so your ball goes in the bucket. For your second shot, use the D-pad to aim your shot, and aim at the peg to the right of the one you cleared on your first shot. To line up your shot: Aim to the left of the peg, then tap right on the D-pad until the shot guide creates a bank off the peg. When you fire, your ball will barely skim the peg, creating essentially a straight angle. Then you just have to time your shot correctly to line up with the bucket. For your third shot, aim at the peg to the left of the peg from your first shot, and use the same strategy as shot 2 to line up your shot.
Trial 6: Wall-Off: Get 3 Off the Wall ShotsUse the super guide to hit your shot off the wall and then into a peg. You'll need to aim high. The super guide makes this very easy. You do not need to land in the bucket.
Trial 7: Five Oh: Clear 50 Orange PegsThis will require some skill. I used Windy the Fairy Flock Master ($1.99 DLC) since I think her powerup is more useful than Bjorn's Super Guide, however this is doable with any Master. You're basically going to have to clear the entire board. My two best pieces of advice here are 1) once the board opens up, you'll likely need to go for at least a few free ball skillz shots, and 2) once you've built a multiplier, try to do shots that combo with a purple peg to get the 25K free ball bonus. This is probably the hardest Peggle Institute trial. If you're having trouble even after 3 or 4 attempts, I'd recommend just continuing playing the main game to build up some skill and coming back to this one later.
Trial 8: Ultraviolet: Score over 500,000 PointsThis is easier than it may initially seem. Super Guide is on the whole time, and you get 8 purple pegs every shot. Use Super Guide to get style points (Super Long Shot shots are an easy 50K. Long Shots and Off the Wall shots are also very good), and use the purple pegs to get free ball bonuses from points and a high score. You don't even need to clear all orange pegs. As long as you get 500K, you'll complete the challenge.
Trial 9: Down Low: Beat the Level Under 175,000 PointsI tried to clear a lot of the blue pegs early on so that they weren't in the way once I had a multiplier built up. I'm not sure if this is the best strategy, but it worked for me. Obviously, avoid the purple pegs and doing style shots. I also left a green peg toward the end so that I could Super Guide my way into a 10K Extreme Fever Bucket without worrying about landing in the 50K or 100K buckets. Also, remember that every extra ball you have at the end of the level will turn into 10K points, so be sure to throw away some balls at the end of the level if you need to. Overall, a little tricky, but not too bad.
Trial 10: Target Practice: Hit All 4 Fast-Moving PegsAim for the pegs when they are toward the side of your screen, rather than the center. The pegs slow down a bit when they're at the sides, and also if you miss, you're more likely to land in the bucket. Other than that, this just comes down to timing it correctly and maybe getting a little lucky, so good luck!
I hope this helped you. Thanks for reading and enjoy Peggle 2