What achievements are impossible without DLC purchases

For every outmatched achievement, I did the exact same thing:

1. Only do the Insane matches (The VHard Hard and Medium Achievements come along with the Insane one)

2. Play on Megatron, it offers a great base that you can hit every enemy from one central position, which leads me to..

3. Play Protos v Terran. Do a standard Cannon Rush: Rush one of your initial probes to the center of their 4 base area.

   Build a few probes while the rusher is in transit. As soon as he his his location you should have enough minerals to build your first pylon.

   The key is to build it far enough from all bases to not bee seen when placing. It cannot be seen when its initially placed, or they will send SCV's at you. If they see it while its building, thats no big deal. They just can't see the initial warp.

4. Wait for the Pylon to complete, then throw down a forge. Wait for the forge, then start placing Photon Cannons at the perimeter of your lone pylon's power range.

5. Rinse and repeat. Just keep placing cannons and pylons to expand as needed. Eventually they will quit as you've damaged their game too much.

Warnings

If you don't damage them enough with the initial few cannons, they will ramp into Mech and you will lose.

If they see you place the forge or the pylon, they will mass attack with SCV's and you lose.

Follow those steps and you will be on your way to Outmatched Crusher

From what I've seen and gained, there is maybe only one that is missable. However, you will have a second chance to get it if you go through a New Game Plus to get that achievement.

Catch

This one is not related to the main story, and is related to another achievement Mystery Stalker. You only meet a certain person 5 times during the game, and after that they are gone. You have to throw a remote controlled batarang at them.