There are four bomb challenges in Spider-Man (PS4)
All you need to do is to go to any of the bombs (you can see the distance between you and the bombs( and then just throw them away in the air and shoot them the combination on PS4 is L1 R1.
Then you do the same thing with the other 3 bombs too.
The challenges and trophies in spiderman are one of the coolest elements in the game i really enjoy having to complete certain tasks and get rewarded with experience or any type of progress in the game. This formula has made me spent a lot of time on the game.