Titanfall

For this achievement, you'll need the Amped Vortex Shield burn card. The best way to get one of these would probably be through buying the Titan Packs (20,000 Credits) in the Black Market, so it might be helpful to leave this to last so you can accumulate points whilst going for the others. Alternatively, keep an eye out on the Daily Deals section, just in case they pop up on there!

Once you have one, don't just use it at the beginning and hope for the best. This can't be done against Titans, and Pilots aren't stupid enough to just shoot you with their primaries, so you'll want to be doing this against the AI. Grunts run away from your Titan, but Spectres just shoot at you with their SMGs.

Wait till about halfway into the game when they start spawning, then activate the Burn Card and be on the look out for large groups of Spectres. They'll start firing at you with, activate the Shield and just hold it pointing towards the Spectre. It takes a couple of seconds to kill with the deflection damage, so it might be useful to equip Minion Detector and try and get a group that are away from the rest of the battle so nothing else can get the kill.

Edit: As a caveat, this pops after the game has ended, and not when you've got the kill. Thanks to BrokenKnight for reminding me!

Edit 2: Some people in the comments have said purchasing the Tactical Ability Pack (20,000 credits) has resulted in more instances of getting the Burn Card needed.

If anyone was wondering :

This can be also done on on Frontier Defense.
Much Easier on the first few waves with grunts and spectres and without any additional Titans to bother you.

Just remember to HOLD while choosing the enemy who fired at you until their shots are reflected and kills them.

Did it this way, yesterday.

There has been a lot of people who aren't getting this achievement to pop and this solution will help clear up a common miss understanding. A friend and I were attempting this achievement and he discovered this.

After obtaining the amped vortex shield from either the daily deals or from a set of burn card packs (I recommend the tactical ability pack since you get 6 cards instead of the 3 from the titan burn card pack and it's cheaper) you should drop your titan while your burn card is active and stand over a group of spectres and use the vortex shield to deflect their rockets/bullets back. Normally, this should be enough to give you the achievement, but this is false. When you get your kill with the amped vortex shield, make sure the kill shows up in a orange color which represents the burn card. If the kill shows up white which represents the normal vortex shield, the achievement will not pop at the end of the match. This is where the confusion happens. The best way to truly do this so you don't waste your amped vortex shield, just go to japan west servers and boost it with a friend. This way you don't need to worry about dieing and you can keep an eye on the kill so you can confirm that the amped vortex shield counted. The guy you're boosting with will see where it says he was killed by the amped vortex shield in the box that appears on the side too.
This has been tested and proven to solve the whole "glitch" achievement problem.

Note: You can now boost 1v1

Credit goes to Creptor5291 for noticing and discovering this method before I did.

In addition to the other good solutions above (use those to get the burn card) once you have the amped vortex I found it easier to the Cheevo in a last Titan standing game.

At the very beginning instead go going for titans, find a bunch of grunts/ spectres, they instantly start shooting you. Activate the shield and make sure you get a kill with it. Cheevo will pop at the end of the match.

Hope this helps.

Here's a quick video guide for this achievement in Frontier Defense. I had kept hold of my AMPED Vortex shield burn card solely for this moment! This is in a custom match with three other players. I didn't manage to call in my Titan during the first wave so I had to wait until the third wave for normal Spectres to spawn. The second wave was full of Suicide Spectres that obviously wouldn't have helped unlock this achievement.

The achievement unlocked after we had successfully defended the harvester and the scores and credits and what not had finished tallying up.

If you're having problems popping this achievement, play Frontier Defence , set up your own custom match on the Backwater map and wait for players to join, once the match starts build up your Titanfall countdown then once it is full commit suicide and active the AMPED Vortex Shield Burn Card. Respawn as a Titan with the Burn Card active and reflect projectiles back at grunts, spectres and titans, just to be safe try and kill/doom at least one of each type of enemy with the AMPED Vortex Shield as I did.
If done correctly the Rejected! achievement should unlock after the match has finished!

After getting the burn card take Conner 193's advice and load a Frontier Defense game on Backwater and wait for players. Use the burn card and get a titan and try hard not to die. I wasn't able to get the pop up on the right of the screen saying AMPED VORTEX SHIELD in orange until i used one nuke titan's bullets to doom another. I think you need to kill one enemy with a different enemies bullets because i had killed a grunt with his own rocket in a previous match and a spectre with his own bullets on a different previous match and neither time the achievement unlocked.