Start up a season game on 0 ego, team doesn't really matter although one with a better pitcher may help slightly. I was able to accomplish this with the Sirloins.
Start by getting two outs and then throwing the ball at three batters so you load the bases. It's only 3 pitches to hit them all as opposed to 12 to walk all three and the batters get a little worried too which helps.
Now the hard part is getting them to not swing at a pitch and take the strikeout. If you throw a couple of balls and work a full count (3 balls 2 strikes) I think they're less likely to swing. Throw a pitch that starts outside of the zone and ends just inside on one of the edges or in the corner and hopefully they won't swing.
I just did this each inning and if they hit or struck out swinging I would try again the next inning. Since you have to complete the season anyway for the other achievements, there shouldn't be any rush! But by trying this you should get it eventually, just keep trying!
Other tips: If your pitcher is tired or really worried, try switching it out for one of your other pitchers. Your closer (CP) is going to have the most confidence in high pressure situations so you'll be able to strike out the batters easier.
This cannot be done against another live player or dummy controller. Thanks to EliteAssassinT7 for testing this.