Having just finished The Idolm@ster for the seventh time and unlocked the final achievement, I thought I'd write up a guide for those of you who'd like to play the game but don't understand the requirements of the achievements. I couldn't find a decent achievement guide anywhere so I tackled it alone. It took approximately 55-60 hours to unlock everything.
Firstly, I'd recommend that you have Japanese reading ability. Hiragana and katakana are a must. Kanji are helpful (as those who learn Japanese will know!) but not necessary to get through the game. I'd also recommend checking out the two FAQs at Gamefaqs for help in understanding the many gameplay mechanics.
Okay, lets get started...
10 Idols - 100 Gamerpoints
Unlocks after you finish the game with all ten idols. As your producer rank goes up after each playthrough, you can begin to make duos and trios. This achievement requires at least five in-game years to complete.
16 Songs - 100 Gamerpoints
Unlocks after producing all 16 songs in the game. Requires a minimum of three in-game years to complete, presuming you don't choose a song twice during that time.
4 Seasons - 100 Gamerpoints
In March, June, September, and December, seasonal auditions will appear in the first slot of 'Special 2' auditions. They require image rankings of 9, 11, 10, and 12 respectively. You then need to attend the promotion on the 'fifth week' of that month, which only appears after successful completion of that month's seasonal audition. You don't need to fill up the bar to pass, you can just put your controller down if you wish.
Super Idol - 100 Gamerpoints
Get your unit to image rank 13, and complete the Super Idol audition in the 'Special 2' audition category. It will unlock on the night right after the audition.
Best Ending - 100 Gamerpoints
You need to get your unit to at least Rank A for this. When you get to the final day of your unit's career, choose the option to tell them the truth. From then each character's dialogue is different, so I'll refer you to the following guide. It's in Japanese, but the character's name is in English in the top-left of the page, and also in the top-right of your game screen.
Audition 100 - 100 Gamerpoints
Unlocks on the night after your 100th successful audition. Very time consuming, as each audition attempt takes around 5-10 mins. This unlocked on my sixth playthrough of the game.
Communication 100 - 100 Gamerpoints
When you do a promotion, selecting certain answers will influence the outcome of the event and give you memories. This achievement will unlock on the night after your 100th successful (Good or Perfect) communication. Refer to the aforementioned dialogue guide for the correct answers for every situation. This unlocked on my seventh playthrough.
Lesson 100 - 100 Gamerpoints
This achievement unlocks after the final summary at the very end of a unit's career, just before it fades back to the title screen. You need to complete any of the lessons 100 times with your meter in the green or orange sections. To stop your idols from quitting the lessons early, get their tension down to yellow or blue levels and try to keep it there. This will also stop lessons from being blocked.
Memory 100 - 100 Gamerpoints
See 'Communication 100'. After almost every perfect communication you'll be awarded five memories. Once the cumulative total from your playthroughs hits 100, the achievement will unlock on the night.
(Secret) True Idolmaster - 100 Gamerpoints
Achieve producer rank 10. To do this, finish each unit's career with a high image level, a high idol ranking (at least 'A' rank), and finish as many special auditions as possible. This took me seven playthroughs to unlock, though you could theoretically do it in five if you knew exactly what you were doing from the very start.
I hope this has been helpful.