My first is the conclusion of all.
My second is the beginning of all.
My third is the requirement of all.
My fourth is the ceasing of all.
Here is my answer:
D O N E
O P E N
N E E D
E N D S
"Done" is a way to describe conclusion (ending) of an activity or experience.
"Open" describes a beginning, as in "the opening number of a show".
"Need" describes a requirement: "You need good grades to get into MIT."
"Ends" is a bit of a stretch, because it's plural, but a "ceasing" is an end.