Mark of the Ninja

You'll almost certainly get this just playing through the game. Anytime you manipulate or hit an object and a guard gets a yellow icon over his head, it counts. This includes breaking lamps with your darts, which you'll be doing approximately four hundred times over the course of the game.

In addition, if you were to do this right after a checkpoint, it will continue adding to your total if you reloaded the checkpoint and did it over and over again. Massive waste of your time, as you'll probably get this naturally by the end of the third or fourth level, but if you wanted to get it ASAP that's your method.

The challenge here would really be finishing the game without having distracted 25 guards using environmental objects.

You can do this right at the start of the tutorial.
Right after you get the grapple hook, there are two guards and a light above them. You get a checkpoint right there.

Grapple to the first ledge. Jump and hit the light.
Each guard counts as one, so you only need to do it 12-13 times right here if you want to get it out of the way.