Since the well-known Threes solvers don't go for this specialty achievement, I wrote one myself, and uploaded it to my github repository: https://github.com/SnapDragon64/ThreesTwelvelockSolver
If you're technically oriented you can compile threes.cc for yourself, but if you're not, the Windows executable should work. It's not the fanciest thing ever, and the win rate is lousy, but at least you can give up after ~150 moves or so, so attempts go pretty quickly.
From the README:
This is an ugly but workable program to help people get the Twelvelock achievement in Threes. (It also works for Sixlock.) Its success rate is only about 4%, but even in principle I doubt much more than 10% is possible. The problem is that all you can do is set up seven of the "12"s, waste a few moves, and hope you get lucky with a "+" card spawn for the last "12".
You should run the program in a folder with twelvelock.txt (a file containing some computed weights for various board features). Hopefully the rest the program is self-explanatory. You just type in whatever info it needs to see the game state, and it tells you what moves to make. You can Undo to the previous board state if you accidentally tell it something wrong. However, if you make a mistake and swipe the wrong Threes direction, you'll have to restart the program. Sorry!
Starting the program from the beginning of the game guarantees its deck counts will be accurate. The other way to guarantee the deck's state is correct is to start the program after making 12N+3 moves, NOT counting "+" card spawns. If the deck is inaccurate, it's not that big a deal, but it will probably hurt the program's predictions slightly.
The program tells you how happy it is with the current game state. It's not the most meaningful number in the world, but 50% is average, 30% or under means the current state probably can't be recovered, and 60-70% means you're heading towards a configuration that lets you wait for a lucky "+" spawn to win.
Note that the algorithm I use will happily try to set up a checkboard of "12"s before ever creating a "96" card, which is kind of pointless (since a "96" is required before "+"s can be "12"s). I could probably have made the heuristics smarter, working in two phases, but oh well. So if you play using the program from the start, you'll probably waste some time making a "12" checkerboard before a "96" is made. But you'll know you have a 4% chance of victory.
My recommended, more efficient, approach to grind for the achievement is to start a Threes game, then play 12N+3 moves (not counting "+" spawns) yourself until you've created a "96" (or the board starts to slip out of control). At that point, start the program and let it try to set up the "12" checkerboard. If it fails and the pretty "12" pattern starts to disintegrate, you should probably just give up and start again.
If you're paying attention, you'll probably notice moves at which you're one "+" spawn away from winning. A "+" spawns with a 1/21 chance, and (as long as "96" is the highest card on the board) has a 50-50 shot of being a "12". So unless you're lucky, you'll see these moves a lot. Good luck! :)