MLB The Show 24

Start a 9 inning exhibition game as the home team. You can pick any team (I used the Dodgers) and I recommend playing a bad team (like the AA Chicago White Sox Affiliate - Birmingham Barons) so it's easier to get the strikeout.
Then put in a relief pitcher and use the quick manage screen to whittle down their energy quickly before assuming control and getting your strikeout.

If you are new to The Show or unfamiliar with baseball, I've included more detailed steps below that should help you.

1) As soon as the game starts, press -> Manager -> Bullpen and warmup one of your relievers (they have less energy) - I used Brusdar Graterol but anyone will do
2) Then go to the 'Quick Manage' tab and walk the first 3 batters (there is a 3 batter minimum rule before you can switch pitchers)
3) Now go back to bullpen and click your warmed up pitcher and put in the game
4) Go back to the quick manage screen and click 'pitch around' when it's your turn to pitch. Pay attention to your pitcher's energy bar in the top right of the screen. When it's the opponent's turn to pitch, press to quickly simulate their half of the inning and continue pitching around until you have 0 energy.
5) When your pitcher's energy is depleted, enter the game and try to strike out the opponent. They can hit and score as many runs as they want and it makes no difference, just make sure not to get them out though so the inning continues. If you end the inning before getting your strikeout, just simulate to the next half inning and try again.

Eventually you should get your strikeout and your achievement will pop!

Other random tips/notes:
-Beginner difficulty, I did not adjust any sliders but you can move CPU contact, CPU power, and CPU timing to the left to probably make it easier. (these can be adjusted mid game if you find yourself struggling)
-You can move Human Starter Stamina and Reliever Stamina to the left too for quicker stamina depletion. I don't think it's necessary if using quick manage.
-I prefer 'pulse' pitching as it's just hitting the button at the right time. You can change that under Settings - Gameplay - to Control - then change 'pitching interface'

Great guide above, but I got this by simply playing a game in the rain waiting for the rain delay and opting to keep my pitcher in after. He was automatically at zero energy after that.

I'm sure the other 2 guides here work just fine. By all means, try their method... I'm sure they can get you the achievement.

I just picked a relief pitcher as my starting pitcher at the start of the game.

I did something a little more simplistic that also allowed me to work on other achievements (going for the long homerun, Hit a double scoring the only runner on 2nd base, Stealing 2nd and 3rd and then getting the RBI, etc...).

Basically any in game achievement, you can work on at the same time as this.

OR JUST GO FOR THIS ONE.

Play an exhibition game (Colorado Coors Field if you want to work on the long HR achievement).
At the pitcher select screen, pick a relief pitcher with the lowest amount of Stamina.

If you want to work on achievements, do so while playing and batting. Keep pitching with the relief pitcher and around the 6th inning he will be out of energy and you can get this achievement. You could also edit the sliders pre-game and make their stamina even lower.

If you don't want to bat and just do this pitching achievement, when you're up to bat go to Quick Manage and Fast Forward HALF AN INNING. That simulates your at bats and only lets you pitch.

Either way, that's how I got it.