Successfully "Passing" a chapter can be easy. In order to do a chapter, you need only the required items and enough energy to do a chapter. Take special note of the mission tips. Normally, the minimal required items will not pass the chapter. You may need more of the required items.
A Passed chapter will be denoted by an open coffin in the upper right of your desired Chapter.
A Failed or unpassed chapter is denoted by a closed coffin in the upper right corner.
Failed chapters are the result of not having the enough of the required items. The Requirements are listed to the right of your desired chapter's picture.
Though simply passing a Mission does not guarantee completion. It may take several attempts before you succeed in completing an entire Mission. To complete the mission in the shortest amount of time, you need to achieve the maximum score for each Mission.
Note that Passing a chapter is only how you determine which chapter you've completed with the Requirements for your desired chapter. Passing a chapter does not unlock a new chapter.