This has been patched on 05/15/18, unfortunately now you need to play the entire game on ego 99. This will not be easy, but can still be done with a few tricks.
1) Attempt this in standard elimination mode as to face the same team in back to back games. While a standard season during the playoffs could also technically work, chances are that you'll face a very good team such as the Moonstars, Nemesis, or Moose and therefore is not recommended.
2) I recommend you play as a power hitting team such as the Sirloins that also have decent starting pitchers and play against a team with very weak hitters/relievers such as the Platypi or very weak hitters such as the Herbisaurs(in this game defense does not win championships). If you don't get the team you like just start a new series.
3) Tweak your lineup before the game. Swap Bashe in for 3rd, Longballo 4th, and Jones 5th for the batting order. Your best batter should always be 4th and you want your highest combined Power + Contact players in the top of the order. For the first game's pitcher swap out Kays(best) with Snugs(worst). You'll use Kays in the second game. If you don't want to play as the Sirloins the same logic applies.
4) In the first game you'll play on a very low ego setting and your main goal is to absolutely trash the other team's pitching staff. You can get away with a max of 2 beanballs against their most dangerous batters and especially pitchers at the beginning of the game to possibly injure them, but be careful as after that the mojo of your own players will suffer. You have to be cognizant of the length of the game, as too long of a game(measured by ABs[at bats]) and the fitness of your own players will drop for the second game. The key to dropping an opposing pitcher's stamina is the pitch count. It's not about hitting homer after homer on the first pitch but rather DO NOT SWING until there are at least 2 strikes. This way you'll earn some free walks and decimate their pitchers' stamina faster. Finish the game once you've drained the stamina and mojo of their entire pitching staff.
5) The timing on ego 99 is insanely fast and takes getting used to. Take a break after your first game and play an exhibition match to practice your pitching and batting on 99. Play a few innings and once you're able to make some contact without giving up runs you're ready to finish your series.
6) Power pitches are a big risk. If you absolutely excel at them go for it, otherwise stick to normal pitches. The advantage of getting pitches in the 70-99 range is greatly overshadowed by the increased risk of absolutely missing a pitch that the CPU sends over the fence. All it takes is one run and that could end your attempt and waste your setup time.
7) Do not pitch anything directly over the plate. Your goal is to have every pitch dance on the outside of the strike zone. Keep the pitches low as the CPU can still hit a perfect 'FOOLED' pitch into a homer, but the odds of this are decreased if the pitches are low. If you let someone get on second base but have one out, I would walk a batter onto first to increase the odds of a double play to get you get out of that inning. With Manny Kays your rotation will look like CB, CH, 2F, then repeat. Do not use the 4F unless it's your only option(relievers). The Curveball is key here as a decent 60+ curveball nowhere near the strike zone still can draw a swing and a miss out of batters. Expect to average 10-12 pitches per inning so you should get 6-7 innings out of Kays, then turn to RP Shay Dee to finish the game.
8) Remember to work that pitch count, try to make the computer throw 15+ pitches per inning. On ego 99 even a decimated pitcher is still not easy but with practice you'll be able to make contact. Don't feel bad if you can't score any runs in the first several innings, as long as you're not losing things are still going okay. This is a marathon, not a sprint. Eventually they will get to the bottom of the barrel in their bullpen and this is where you will capitalize on the opportunity. There's a good chance you'll win this game with only a handful of runs maybe even one, and that's all you need.
9) Use power swings with everyone except Addonomus and Rush. With these two guys their contact is so low that unless you get great/epic contact the ball isn't going anywhere, so use contact swings with these guys(or your other <20 contact players for a different team).
10) Don't even bother swinging with your pitcher. Honestly your chances of getting a base hit let alone anything meaningful are so low that they're actually more useful just standing there to make the CPU throw 3-6 pitches to either get them out or if you're lucky walk them. Usual baseball logic applies that if your pitcher is tired and will just be replaced next inning then pinch hit for them with Betty Sparks.