1. Collectibles
1.1. All Suits
1.2. All Black Cat Journals

2. Story-Related
2.1. Friendly Fire (Maximum Carnage)

3. Miscellaneous
3.1. I’m on a Roll! – Achieved a combo streak of 42
3.2. Sneaky – Completed a hideout without being spotted
3.3. Aerial Break – Destroy any armored enemy using Web-Strike
3.4. Luchador! – Completed all combat challenges

Fashionista
Unlocked all suits
There are a total of 13 Suits (Costumes) in The Amazing Spider-Man 2.

Here is a list of all Suits and how they can be unlocked:

#1 – Vigilante: Available from the Beginning
#2 – The Amazing Spider-Man 2012: Available from the Beginning
#3 – The Amazing Spider-Man 2014: Available from the Beginning
#4 – Superior Spider-Man: Beat all Combat Challenges
#5 – Ultimate Comics Spider-Man: Obtained automatically during Story
#6 – Big Time: Clear Russian Hideouts
#7 – Scarlet Spider: Clear Russian Hideouts
#8 – Spider-Man 2099: Clear Russian Hideouts
#9 – Flipside: Clear Russian Hideouts
#10 – Spider-Armor: Clear Russian Hideouts
#11 – Hornet: Complete All 15 Races
#12 – Ricochet: Obtained automatically during Story
#13 – Spider-Carnage: Beat the Story

Lover
Retrieved all parts of Black Cat’s journal
There are a total of 10 Black Cat Journals (Audio Logs) in The Amazing Spider-Man 2. Finding all of these collectibles will earn you the Lover Trophy or Achievement.
All the other Audio Logs are not needed for any trophies or achievements and can be ignored.

Five of Black Cat’s Journals can be found during Story missions. The other five are hidden in the open world. If you fully upgrade your Spider-Sense they will be highlighted on the mini-map when you get close to them.

In the Pause Menu under the “Messages” tab you can see exactly which logs have been found. Each one has its own number, so that you can keep track of what’s missing.

Friendly Fire
Damaged Carnage with fire at least 3 times before defeating him
Mission: Maximum Carnage
During the Carnage boss fight you can activate levers around the room to unleash a burst of fire near them. This must be done in the second half of the boss fight, after Cletus Kasady turns into Carnage. Simply stand under the levers, wait for the boss to get close to you and hit L1 (PlayStation) / LB (Xbox) to pull them. When Carnage jumps up the wall you should activate all the levers around the room and hit him with a Seismic Blast to make him fall down into the fire.

Please note: you can replay all missions by going back to your home via the open-world Metro. There are several pictures on the bedroom wall that serve as mission select.

I’m on a Roll!
Achieved a combo streak of 42
This can easily be done during the combat challenges. Combat challenges can be started at the arcade machine in Stan’s Comic Book Store (marked with a blue book-symbol on your map). In fact, while playing through all 12 challenges there is a good chance you will unlock this naturally. The easiest way, however, is to repeatedly attack the last remaining enemy of a round with the Web-Strike (R1 on PlayStation, RB on Xbox). The Web-Strike doesn’t actually do any damage, so you can keep doing this indefinitely.

Sneaky
Completed a hideout without being spotted
There are 5 Russian Hideouts and they are displayed with a purple eye-symbol on your map. They will show up automatically after making some progress in the story. Go to the most southern one as it is extremely easy and quick. Once you are inside, web-rush to the ceiling and you should see the target below you (a container with a new suit). Simply take out the nearby guards and go to the container to finish the hideout.
It is essential that the Awarness level (the bar in the top left corner of the screen) stays at zero. Only then you will get the trophy / achievement.

If you raise your awareness level, be sure to pause the game immediately and click restart. The hideouts disappear once you’ve completed them!

Aerial Break
Destroy any armored enemy using Web-Strike
Mission: The Kingpin of Crime!
Shortly after this mission starts you will encounter your very first armored enemy in the game. You will be given a short text tutorial. To disable an enemies armor you have to press Circle (PlayStation) / B (Xbox) repeatedly. Do this until all the yellow heavy armor disappears. To get the trophy / achievement you now have to attack with a standard Web-Strike (R1 on PlayStation / RB on Xbox). You don’t have to kill the enemy with the Web-Strike.
Please note: you can replay all missions by going back to your home via the open-world Metro. There are several pictures on the bedroom wall that serve as mission select.

Luchador!
Completed all combat challenges
There are a total of 12 combat challenges. You can play them by interacting with the arcade machine in Stan’s Comic Book Store (the store is marked on your map with a blue book-symbol).
The arcade machine becomes available after the first couple of mission, but you cannot access all challenges until much later in the story. Each challenge consists of 4 waves of enemies. If you die during either wave, you have to restart the current challenge. You can also leave the arcade machine and continue another time.

Before doing this you should definitely buy the majority of upgrades. Your suit should also be maxed out. It’s a good idea to wait until after the story before even attempting the challenges. They aren’t too terribly hard, but require a good understanding of enemy attack patterns.

Keep in mind that you can heal yourself by pressing ↓. Make use of this in between the waves. You can also set the difficulty to Human (Easy) in the game settings. The only difference between the difficulties is that you take more damage.