Make no mistake, this achievement will take many hours (it takes me 4-8 hours for one season alone) to obtain and is the most time consuming achievement in the game. Also, none of your accumulated My Player stats count for the collection achievements (such as Fanning the Flames) nor can you obtain any ingame achievements (such as Take That) due to the fact that the games are technically simulated. However, you can obtain 11 achievements while playing through this mode and this achievement requires you to complete a number of goals and retire, making it into the Hall of Fame. This guide will cover all the My Player achievements (if you simply want this one, simulate until you get your required goals).
Under the main menu, go to My Player. You will then be asked to create your player and what type of player he will be. I used the Slugger type, which makes it easier to get hits as well as work towards the career goals but it's not required. It's also extremely easier to choose a batter rather than a pitcher as most games as a hitter will take you between 5-10 minutes and you'll get much more opportunities to earn stats and work towards your career goals and achievements. You'll also be asked which team you want to be on. If you choose a somewhat bad team, you'll get The Top achievement much easier, but you risk missing the playoffs if you do horribly (you can always exit out and retry games you lose as long as you don't exit to the menu first).
You'll then start in the minors. The first thing you'll want to do is change the sliders in your favor (though editing down CPU sliders will affect your teammates so be careful). It will help you get more hits as well as boost your stats easier. I recommend playing every game just to get used to the concept (playing key moments and batting or pitching) as well as build your stats. Once you meet all your call up goals, you'll unlock The Call.
From here, you can continue to play each game and build your stats (you'll also get a 2X multiplier if you get a ten game hitting streak) or start simming towards the end of the season. I highly recommend that you play each game in your first season to build stats as well as work your way to a playoff spot and the A Job Well Done achievement (plus it's only three months worth of games rather than a full season anyway).
If you do well, you'll likely become the player of the game, earning you the Your Day achievement. If you simulated, you may run into a clutch moment. If you succeed in the goal, you'll increase your clutch rating and earn the That's Why I'm Here achievement.
Once you get to the end of the season, you'll know whether or not you made it to the postseason. If you won most of your games, you'll unlock the A Job Well Done achievement for winning 100+ games in a season. To wrap up your first season, play through the postseason and win the series, which will unlock you What's Your Ring Size? By this point, you should have unlocked all your required season and team goals and should only need your career goals to make the hall of fame (if not, you'll get them for sure next season).
You should be regularly upping your stats along the way, making your overall rating climb. Once you top your team's best player, you'll unlock The Top (though you'll likely get this during your second or third season). Once you start your second season, you'll notice that you have a team season goal (if you won the series, this will likely be "Win back to back series"). If you complete this goal, you'll unlock The Goal achievement.
Now is the time to start simulating. You're more than welcome to continue playing, but once your stats start to get high, your player will start to do well and earn xp on his own. You'll still be required to play key games (any game that is against a rival, on opening day, against someone with a key player at your position or an award rival) as well as clutch moments (netting you This is Why I'm Here if you haven't got it already) but this will chop down the time considerably.
Unless you're not doing well, by the time you get to July you will likely be invited to the All Star Game. Once the game officially invites you to play it, you'll unlock The Star. Keep simulating games and playing until you make it to the postseason again. Once you win the second series in a row, you'll unlock 2-Peat (as well as The Goal if your goal was back to back series).
Once you start your third series, you'll want to get traded to another team (preferably a rival or someone that plays your current team frequently) so you can get the Payback achievement (you can always trade yourself back as long as you do it before the trade deadline in July). To do so, go into your career decisions and choose the team you want to be traded to and press Start. You should automatically get traded to that team.
At this point, you should have all the My Player achievements except for The Hall. You should also have all your season and team goals and at least one career goal (though you could have more). If you're missing any achievements, now is the time to mop them up and try to get them. If not, just keep simming your seasons away and attempting to fulfill any career goals that seam feasible (the easiest ones are the 2 MVP awards, 300 HRs, 300 SBs and 1000 RBIs, though you're free to try for any of them). Depending on how your stats are, you should automatically get three by the end of the sixth season anyway (6 seasons of .290 batting or over, 6 seasons of .800 OPS or over, 5 seasons voted to All Stars). Once you finish all your career goals, you should have the option to retire (under the career decisions menu) and this achievement will unlock as soon as the game saves.
One thing to keep in mind is that if your profile should ever corrupts, you have to restart My Player (for some reason it won't unlock earned achievements if you restart your profile). One tip is to turn off autosave in the main menu as well as making sure you wait until both your career and your profile save after each autosave/save (if you turn your system off after your career saves, you'll likely corrupt your profile as the game autosaves your profile afterwards). Once you get this achievement, pat yourself on the back as this is a very time consuming grind.