All credit to go to Tveilor for his Marvel's Spider-man guide.
As the trophy says unlocking it requires you to purchase all the suits. You unlock most suits by levelling up but some of them by do certain tasks. I'll list all suits and how they unlock and appear.
- Adanced Suit - Story Mission - 1 Backpack Token, 1 Crime Token
- Classic Suit (damaged) - Story Mission - Free
- Classic Suit (repaired) - Story Mission - 2 Backpack Tokens, 2 Crime Tokens
- Noir Suit - Story Mission - 2 Backpack Tokens, 1 Base Token
- Scarlet Spider Suit - Level 4 - 3 Crime Tokens, 2 Landmark Tokens
- Spider Armour MK II Suit - Level 5 - 1 Base Token, 1 Landmark Token, 2 Research Tokens
- Secret War Suit - Level 7 - 2 Backpack Tokens, 1 Base Token, 2 Research Tokens
- Stark Suit - Level 9 - 1 Base Token, 3 Crime Tokens, 1 Reseasrch Token
- Negative Suit - Level 11 - 1 Base Token, 2 Landmark Tokens, 1 Research Token
- Electrically Insulated Suit - Level 13 - 1 Base Token, 3 Crime Tokens, 1 Research Token
- Spider-Punk - Level 16 - 2 Backpack Tokens, 3 Crime Tokens, 2 Landmark Tokens
- Wrestler Suit - Level 19 - 2 Backpack Tokens, 2 Base Tokens, 2 Research Tokens
- Fear Itself Suit - Level 21 - 2 Base Tokens, 6 Challenge Tokens, 3 Research Tokens
- Stealth ("Big time") Suit - Level 23 - 2 Base Tokens, 4 Challenge Tokens, 3 Landmark Tokens
- Spider Armour MK III Suit - Level 26 - 2 Base Tokens, 4 Challenge Tokens, 4 Crime Tokens
- Spider-Man 2099 Black Suit - Level 29 - 2 Base Tokens, 4 Crime Tokens, 4 Research Tokens
- Iron Spider Suit - Level 31 - 3 Base Tokens, 3 Challenge Tokens, 4 Crime Tokens
- Velocity Suit - Level 33 - 2 Backpack Tokens, 4 Challenge Tokens, 2 Landmark Tokens
- Spider Armour MK IV Suit - Level 35 - 4 Base Tokens, 4 Challenge Tokens, 3 Landmark Tokens
- Spirit Spider - Level 37 - 6 Base Tokens, 6 Challenge Tokens, 6 Crime Tokens
- Spider-Man 2099 White Suit - Level 39 - 4 Base Tokens, 4 Challenge Tokens, 4 Crime Tokens
- Vintage Comic Book Suit - Level 41 - 4 Backpack Tokens, 4 Challenge Tokens, 4 Crime Tokens
- Last Stand Suit - Level 45 - 20 Crime Tokens
- Hidden Suit - Reward from getting 100% in the game - not needed for this achievement
- Homemade Suit - Find all backpacks
- Anti-Ock Suit - Story Mission - Free
- Dark Suit - Complete all Black Cat Stakeouts - Free
- ESU Suit - Complete all secret photo ops - Not required for this achievement
To also make this a bit easier try to not spend the base or challenge tokens until you can unlock all the skins as if you don't have enough you're required to get a higher score in the challenges then and they aren't easy.