Yes, saying "Most of Shakespeare’s greatest plays..." is perfectly correct. And your second sentence is also correct, but without the leading "The". However, you need to add the word "the" in between "between" and "years". The following sentences, however, have different meanings. Most of Shakespeare’s greatest plays were written between the years 1590 and 1612. -> Most of his greatest plays, but not all. Shakespeare’s greatest plays were written between the years 1590 and 1612. -> All of his greatest plays, not just most.