You'll encounter Test Your Strike challenges in the Challenge Tower, which can be accessed from the main menu. The final Test Your Strike challenge that you have to beat for the achievement is challenge #168 in the Challenge Tower.
Test Your Strike works basically the same way as Test Your Might, only a lot more precision is required. You have to press the A, B, X and Y button to increase the red meter (Might). There will be an area marked on the bar, and it will say "(Left trigger symbol) (Right trigger symbol) Break" to the right. In Test Your Might, you only have to get the Might into the marked area. In Test Your Strike, you must get the Might between the two arrows that are within the marked area. Once you hit the "Sweet spot" between the two arrows, the Might turns from red to green. From here, you can wait for the time to run out, or you can press the LT or RT to immediately finish the mini-game.
I've found that the best way to do this is to mash all four action buttons (A, B, X, Y) until the Might has risen above the marked area. From there, I only start mashing one or two buttons, letting the Might slowly start sinking down until it reaches the sweet spot, at which point I keep it there until the time runs out. You can press the LT or RT to instantly deliver your attack, and end the mini-game, but I don't recommend this. In that split second that it takes you to hit the LT or RT, it's very easy for the Might to slip out of the sweet spot, especially in the later challenges. Additionally, I find that the mini-game is a little more forgiving once you've reached the sweet spot; it'll allow the Might to go a little below the arrows, or a little above.
If you're going to down vote, I'd appreciate it if you took a few seconds and left a comment telling me why. Thanks!