There are total 13 Suits / Costumes in this Game (without preorder & DLC). Only this 13 counts for the Achievement.
Here is a list with the Requirements and the Timeline for the Video below.
00:06 -
Vigilante (Available from the Beginning)
00:30 -
The Amazing Spider-Man 2012 (Available from the Beginning)
00:54 -
The Amazing Spider-Man 2014 (Available from the Beginning)
01:17 -
Superior Spider-Man (complete all Combat Challenges)
01:44 -
Ultimate Comics Spider-Man (automatically during Story)
02:14 -
Big Time (Complete a Russian Hideout)
02:43 -
Scarlet Spider (Complete a Russian Hideout)
03:11 -
Spider-Man 2099 (Complete a Russian Hideout)
03:44 -
Flipside (Complete a Russian Hideout)
04:15 -
Spider-Armor (Complete a Russian Hideout)
04:43 -
Hornet (Complete All 15 Races)
05:16 -
Ricochet (automatically during Story)
05:43 -
Spider-Carnage (Complete the Story)