There are five fan clubs you need to join for this achievement.
You only need to join for this, not complete their questlines.
Genesis Fan Clubs (2)
Red Leather
As soon as chapter 2 and as late as 7.
In Sector 8-Fountain speak to one of the three women to the right of the fountain.
She will ask if you want to join, say yes.
You will get a mail for confirmation.
Study Group
As soon as chapter 2 and as late as 7.
In Sector 8-LOVELESS Avenue near the back of the hub.
She will ask if you want to join, say yes.
You will get a mail for confirmation.
Angeal Fan Club (1)
Keepers of Honor
As soon as chapter 2 and as late as 7.
In Sector 8-Fountain speak to one of the three women to the right of the fountain.
She will ask if you want to join, say yes.
You will get a mail for confirmation.
Sephiroth Fan Club (1)
Silver Elite
Chapter 5 only.
In Sector 6-Park, near the Church hub there is a woman hiding behind a structure.
She will ask you three questions. The answers are:
Masamune
Super Nova
Left-Handed
You will get a mail for confirmation.
Zack Fan Club (1)
This is the hardest to do and it's highly missable.
In Chapter 6 only you get a mini-game defending Junon.
Make sure to get all 30 enemies with no escapes as I do believe this has something to do with triggering the fan club.
After that and before you move on to the boss, the the cable car directly across and speak to Cissnei who will say something about disappointing your fans.
After returning to Midgar go to the entrance level of the Shinra building and speak to the receptionist on the left.
Join the club and you will get a confirmation mail as well as the achievement.