UPDATE (12/11/2014): According to comments on the Solution, the 'Can't Win' Medal has been fixed. The previous problem was that you could only gain this medal while on Windows 8, but this is no longer the case and as such every medal can be unlocked with just a Windows 8 Phone.
There should be an update, but if there is not and the Medal is still glitched for you, Uninstall the game and redownload it to force the update to be automatically downloaded. Progress is saved to the Cloud.
WARNING: It has been found that apparently if the 10th or 20th Medal you obtain is achieved on Windows 8, this will lock you out of both Achievements respectively; this includes the 'Can't Win' Medal.
Note for Odd Achievement haters: The Windows 8 version of Mahjong has 25g, which can be a negative for some people who do not enjoy games that have odd Achievement totals. You can very easily obtain the 'Can't Win' Medal without accidently getting an Achievement, as long as you don't win a game, due to how the Medal only requires you to lose 3 games, and not win any. There is also an Achievement for changing the theme on the computer, so if you want to avoid this, do not change the theme either. You can delete the game off your card on your Console due to the fact you have zero Gamerscore.
The Medals are a separate list of 'Achievements' that are for accomplishing tasks on both Windows Phone and Windows 8. There are some Medals that are on Windows 8 that are not on the phone that apparently count towards the total of this Achievement, but there have been many reports of the game glitching through using these, so we are going to only focus on the ones that are located on the phone, with the exception of the 'Can't Win' Medal, that has to be obtained on Windows 8.
A lot of the Medals are made easier due to the fact you can abuse the 'Hint' option indefinitely. By pressing the outer edge of the screen a popup will appear at the side of the screen with Icons, by pressing the light bulb Icon you will be shown two Tiles that will glow, if you continue to do this and only do the matches that the game tells you to do, it is nearly impossible for you to fail the game.
Castle Crasher - Complete the Castle puzzle without using undo and where your first move is a reshuffle.
Castle is the second Hard Puzzle; you will need to have beaten Nautilus in order to unlock it. At the bottom left of the screen, there is a button that says 'Shuffle' by pressing this you will shuffle the Tiles into a different position (This can only be done once per game), after doing this, just abuse Hints to easily finish the game.
Space Train - Complete the Train puzzle using the Cosmos theme 5 times.
To change the theme, go to the main menu and swipe right until you get to the tap labelled 'Themes', the default theme is Underwater, so you will want to change to Cosmos for this one. There is a later Medal for completing 10 Puzzles on hard without using reshuffles or undos, you can easily achieve five of those with this Medal if you abuse the use of Hints.
Climbing the food chain - Complete the following puzzles in sequence: Butterfly, Turtle, Ray, Dragon.
The Butterfly is the fourth Medium Puzzle, the Turtle is the first Easy Puzzle, the Ray is the third Extreme Puzzle and the Dragon is the first Extreme Puzzle. Once completing the correct puzzles to have these all unlocked, simply play each one in order that is listed in the Medal, making sure to make good use of hints.
All the Right Moves - Complete 10 puzzles on Hard difficulty without using a reshuffle or undo.
You could possibly already have 5 of these from doing the Train Puzzle for a previous Medal, but either way you will probably have to attempt this. Use hints to easily win.
Can't Win - Reach "No More Moves" three games in a row on three different puzzles.
Normally I would suggest using hints, but I found that I was so bad at the game that if I attempted to play the game legit I would fail very easily. If you find that you are about to win, you can do many different things; you can choose to shuffle the playing field, rewind the pieces so that you can take a different route with matching, start a new game with the same board, or leave the match and start a different Puzzle. If you leave the game or Start a new game, it will not count as a win or a loss and as such will not count against you on the Medal. After losing 3 games the Medal will unlock.
The Real Tail End - Complete the Nautilus puzzle where the last match you make contains a Tile from the tail end of the spiral.
The Naughtilus Puzzle is the first Hard Puzzle. The Tail End is referencing to the bottom left of the spiral where you can see that the line of Tiles comes to an end. The tail is stacked 3 times so you have some leeway while trying to avoid losing the tail. I used the second to last Tile on the tale, but I do not know how far is considered the Tail End, but to play it safe try to focus on the last 3 Tiles. If you come to a position where the only possible move is to use the last Tile on your tale, you have one chance to reshuffle the game, and hopefully get a better Tile position.
Dragon Slayer - Complete the Dragon puzzle without using a reshuffle or undo.
The Dragon Puzzle is the first Extreme puzzle; by using hints you will not run into any problems, unless you accidently tap Undo instead.
Photo Finish - Complete a puzzle within three turns after using a reshuffle.
Play any puzzle as normal using hints until you have only got 6 Tiles left on the field. At the bottom left of the screen is a small icon that says 'Shuffle' press this and confirm to shuffle around the available Tiles, now simply made 3 matches and the Medal is yours.
Go Wild - Make three consecutive matches with wild Tiles.
Wild Tiles vary in appearance between themes, the default theme is Underwater, and the Wild Tiles are Silver and Gold. You will most likely get an opportunity to get this Medal while grinding out the other Achievements/ Medals, so there isn't really any reason for you to go out of your way to try and achieve it. Just keep in mind that you are on the lookout for this while playing each game. Using hints, skip over the hints that involve the use of Wild Tiles, unless there is no other option; when you are at a position where you have 6 wild Tiles that you can use, match them one after another to get your Medal.
Well Travelled - Complete a puzzle while using each of four different themes.
The only theme that does not have an Achievement/ Medal tied to it is the Autumn Glade, so this is the only theme you'll have to go out of your way to use. Please note that the Medal using Tranquility does not actually require you to finish the game you start, so it's possible to miss that one.
Little Wingman - Make 100 Matches.
This should be unlocked after about 2-3 games. You will definitely get this Medal while going for the rest of the Achievements/ Medals.
Mighty Matchmaker - Make 1000 matches.
This should be unlocked after about 20-30 games. You will definitely get this Medal while going for the rest of the Achievements/ Medals.
You're Basically Cupid - Make 10,000 Matches.
No matter how hard you try, you are very unlikely going to have enough matches made after going for every other Achievement/ Medal. I would suggest playing Easy Puzzles, as these usually allow you to make matches quicker. Using hints will make this a lot quicker. Note: If anyone has a quicker method of doing this Medal, please let me know
True Expertise - Complete four different puzzles in the expert category.
There is a Medal for completing four Expert puzzles using the Underwater theme. Although that Achievement does not require the puzzles to be different, you can get both that Medal and this one at the same time if you do not change your theme after starting the game (Underwater is the default theme)
Super Speed Runner - Completed 25 puzzles in under 3 minutes each.
When using hints, it will be very common to finish games this quickly, especially on the easier Puzzles. If you want to get this out of the way, simple play any of the Easy Puzzles and use hints to quickly get matches.
Quick Thinker - Make 5 matches in under 15 seconds.
If you are constantly abusing hints, this is a very easy Medal. You will most likely get this without even trying as you have to make a match every 3 seconds, a very easy task on some of the easier Puzzles.
Master Scuba Diver - Completed 4 expert puzzles using the underwater theme.
The Underwater theme is the default theme when you first start the game. You have to complete all 4 of the expert puzzles for another Medal, so you might as well do them while you have the correct theme equipped.
Man of the Hour - Acquire at least 60 minutes play time on each difficulty.
You can view your total play time on each difficulty by going to Statistics. It is likely you might not have 1 Hour on each Difficulty, due to some not having as many Achievements/ Medals, meaning you'll spend less time playing them. You have to grind 10,000 Matches, so if you want to get this while doing this, you might as well just play one Difficulty matching Tiles until you reach 60 minutes, then switch to another Difficulty.
Wind Waker - Using the Tranquility theme, matched the following Tiles in sequence N,E,S,W
Choose the Tranquility theme on the main menu and start a puzzle on either Hard or Extreme; I personally used Crossing, as I found this had a lot of pieces and would give me more of a change to keep the pieces I needed. The letters are not too obvious and are found on the top left of the Tiles. Simply use hints to get rid of pieces that do not have letters on them (By pressing the hint button several times you can skip past suggestions that include Tiles you want to keep) Make sure you cycle through all the available hints to check which are actually matchable. Once you have a piece with N, S, E and W, simply match them in the correct order to receive your Medal. There is a Medal for winning a game using each theme, so this might be a good opportunity to do so by finishing the game you've started, as there is no other reason Medal/ Achievement wise to have this theme selected.
Pro Landscaper - Complete the Bramble puzzle 20 times.
Bramble is the fourth Expert puzzle. In order to unlock Bramble, you need to have completed the Dragon, Complex and Ray puzzles. Bramble is quite a long puzzle, but by using hints this will progress quicker.