This page of Marvel's Spider-Man Game Guide contains a walkthrough for What's in the box? mission. This time you will unlock another side activity, that enables the use of challenge tokens.
Get to the location marked on the map. Watch a cutscene where you'll meet the Taskmaster. A mysterious stranger will check your skills in a variety of tests - the map will show you his challenges. Some of them are definitely among the most difficult missions in the game.
Take part in the challenge that is ahead of you. In this case, you must reach three bombs, catch them with your web and detonate them in the air. The task is complicated by the fact that you have little time for everything. What's more, you can complete this mission to get bronze, silver, or gold medal - all depends on the result you get at the end of the mission.
The Taskmaster evaluates, among other things, the bonus for web used, the amount of time you have left, etc. You will always get at least one challenge token for each completed challenge - you'll need a lot of those to create new costumes. Fortunately, you can repeat these missions and try to achieve a higher score in them.