His greatest accomplishments were as the greatest body builder to ever live.
Arnold has won the highest honor in bodybuilding, the Mr. Olympia contest, 5 times. He has also won numerous other body building contests.
Arnold was the man who revolutionized bodybuilding, and turned it from a small sport whose competitors also had day jobs to a sport in which every contest paid enough for the competitors to make a living at the sport.
For anyone familiar with bodybuilding Arnold was also probably the first truly large bodybuilder. He was the first contestant in an American contest to weigh in at over 250 pounds. At over 6 feet tall this makes him a monstrous person. Most of the other contestants in the major events were around 200 pounds and were under 6 feet tall.
As far as acting goes, people often refer to him as a bad actor. However, supposedly in his home town in Austria as a young man he was a very good Shakespearian actor.
I watched his A/E biography