"Made from nitrogen" is wrong. "X is made from Y" means that some kind of process transforms Y into X. My shirt is made from cotton, steel is made from iron, her chair is made from wood.
"Approximately eighty percent of the Earth’s atmosphere is made of nitrogen" is correct. Here are some other ways to say it.
"The Earth's atmosphere is 80% nitrogen."
"Nitrogen makes up 80% of the Earth's atmosphere."