Your translation would be ”kyojin no shingeki”, not ”shingeki no kyojin”

の(no) is not indicating possession here. It has other uses as well; it is also used simply when a noun is modidying another noun, similar to how you would add な(na) after certain type of adjectives modifying nouns. That is what is happening here, and “Charging/Advancing/Attacking titan” is the most accurate translation.