Taptiles

The key to getting this is the Gem Mode and the Wild Tiles.
When you enter Gem Mode (turn all the blocks green), you can use multi-touch for fast selection. I used two fingers on both hands, tapping like crazy around the edges of the board looking closely for Time Tiles and Wild Tiles. Doing this I was getting up to 4 boards cleared per green, which can add close to a full minute per Gem Mode.

If you hit round 25 and are not over 4:30 on the clock, give up and start again. The board difficulty and reduction of the bonus to 10sec make it impossible to gain enough time.

This is actually very easy, provided you have a touchscreen.

The game does no penalize you for selecting tiles that don't match. So just tap like crazy with all ten fingers all over the puzzle. Most puzzles can be cleared in two or three seconds using this method. Some will be harder, with some you will probably have to slow down or rotate the view... but in most cases it will work.

I got this on my first try, actually.

You will get GEMOLOGIST at the same time, since clearing the puzzle in gem mode using this method is SUPER FAST.

Alright, so here's a way that I thought of, which would make this achievement actually possible with a mouse for most mouse users ( hats down to all those who got it with the mouse completely legitimately ). So, I thought that since touch screen users have the big advantage of tapping in multiple places at the same time, I figured I could get mouse users closer to that by creating a macro command that basically continuously clicks the mouse (about 30 times per second) at the current cursor position as long as you hold down a key.

You'll have to download AutoHotKey ( http://www.autohotkey.com/ ) and create in your Documents folder a file called " Autohotkey.ahk " and in it (through Notepad) copy the following content:

$F1::
Loop
{
if not GetKeyState("F1", "P")
break
Click
}
return

Save the Notepad and go to C:\Program Files\Autohotkey and launch Autohotkey.exe ; you'll see a white H in a green square in your tray, letting you know the script is active (but does nothing as long as you don't press the "F1" key). Right click on that H to see what options you have while Autohotkey is running, just to get a bit more accommodated with the program.

As you might be able to tell, as long as you hold down the "F1" key on your keyboard, you will constantly click at the current cursor position; once you let go of "F1" it stops.
The idea is that when a board shows up that looks easy to complete, but it would just take too long to drag the cursor back and forth precisely, then you can just hold down the "F1" key and move your cursor all over the board and with a bit of luck you'll get combos really fast one after another. It also works on more complex boards, but not to the same extent, because sometimes you really have to match 2 specific tiles and you're just not accurate enough if you constantly click in between the 2 specific tiles, so at that point, I recommend letting go of the "F1" key and manually make those specific matches, clear up the board to free up some tiles and then you could "F1" all over for a potentially quick finish.

This little trick will certainly NOT make this achievement a walk in the park for mouse users. It will NOT get you to the same level as touch screen users because you are still limited to clicking at a single point at a time, however by clicking so fast and moving your mouse all over the place you almost simulate clicking in multiple spots at almost the same time, just like touch screen users tap with multiple fingers in multiple places, though they can do it at the exact same time. Firstly, you still have to get lucky with board layouts and be good yourself at spotting matches quickly in complex boards and secondly, you still need A LOT of Gem Tiles to show up accompanied by Wild Tiles, otherwise you will struggle, stale or worse, fall behind. It will still take a lot of tries to do this, so don't get demoralized if you don't succeed in the first few shots. You need to get used to using the "F1" key properly, find whether it's better to move the cursor in a circular fashion or just vertically or horizontally as you're constantly spinning the board; it all depends on the layout of the board, try different cursor movements until it works, otherwise do a few manual matches to free up some tiles and then try "F1" again. Moreover, you still have to focus a bit on specific pairs as you're dragging the mouse all over the screen, hoping to get other matches alongside the one that you've eyed. The "F1" key works absolutely best during Gem Mode; then you'll really see the speed of the matches if you're moving the cursor right.

I suggest that when Time Tiles show up, you take one second to make that match between them right away (if possible) and also when Gem Tiles show up, if the board is easy, activate them at the end of the board, otherwise just activate them as fast as possible. As for the Wild Tiles, during Gem Mode, if you think Gem Mode will end before you get to clear the whole board and leave the Wild Tiles for last, then simply activate the Wild Tiles right away, otherwise leave them for the last match of the board in order to instantly finish the following board (see Gemologist for details).

I also recorded a successful run so as to prove this is truly possible and that not all hope is lost for mouse users. I already had unlocked the achievement when I recorded that video; the achievement unlocks as soon as the timer goes over and including 5:00. I also did not watch the ad/commercial in the beginning because that system is currently broken (at least for me) and will not play any ad and it also won't give me the 30 extra seconds. If you have any questions or remarks, leave them in the comments.
NOTE: This trick will make the Gemologist achievement also possible for mouse users, as well as some really complex Expert difficulty Daily Challenges. The video is not sped up, even though it might look like it; it's just recorded at 60 FPS. Yes, there's no audio and there are a few lag spikes now and then.

I just did this with a mouse. It's extremely tough and you absolutely need to get lucky with the green gems. I got to 5:15 before I paused because my index finger was aching so much. I also only lost my streak ONCE.

There's no real reason to try this with a mouse unless you can make matches fast enough. I have been playing this game on and off for a few months, completing most of the challenges (apart from a few 4 star mix and match ones), but I still couldn't do it without a technique. Until yesterday I was trying to clear boards without a tactic and I couldn't even breach 4 minutes. Then I started concentrating on the Gemologist achievement, and once I nailed that I found that I was breaching 4 minutes every 2nd or 3rd attempt. Getting the technique of Gemologist down is very important.

A few tips:

0. Watch the ad. Seriously!
1. Disable the drag and rotate thingie with your mouse in the game settings.
2. Use A and D on your keyboard to rotate 45 degrees left/right when you start running out of matches on your current POV.
3. Obviously take the hourglass powerup immediately, but save green gems and wilds, always. If you get lucky enough to get green gems and wilds on the same board as the end pieces, activate green gems and then wilds, otherwise just activate what you're left with.
4. Something that annoyed me, especially in green gem mode, is that if I clicked and released the mouse button too fast, the game would not register it. I don't know if it's just my computer, but I had to basically reprogram my brain to hold the mouse button a slight bit longer while in green gem mode, but once I got the hang of it I got 9/10 clicks to register correctly.
5. In green gem mode, on the more tricky layouts (with "stuck" blocks), I tried to clear out the "non-stuck" blocks as fast as I could in hopes of keeping my streak and getting more bonuses.
6. And most important of all, BE ALERT! Don't try this when you have your mind on other things, feel drowsy, etc. You WILL fail, lol.

In the end it's a lot about luck, but it is doable. You will most definitely need a ton of practice and persistence. Or enough money to buy a tablet