Here is the full list of all 20 The Amazing Spider-Man achievements worth 200 gamerscore.
Jump over 20 obstacles while running
Wall climb a total of 3 kilometers
Web-sling a total of 5 kilometers
Use 5 tonics
Shoot 30 web projectiles
Defeat 20 enemies
Avoid 10 attacks
Take 5 photos
Reach Level 5
Meet the Lizard (Mission 12)
Get your powers back (Mission 18)
Defeat the Lizard (Mission 26)
Collect 1500 Spiders
Learn 20 skills
Defeat 15 enemies with the Super Attack
Earn the Gold rank in all random events
Save 15 citizens
Dismantle 10 bombs
Acquire 20 of each collectible
Finish all Challenges