To accomplish your goal means to complete it. When you run a race, you accomplish your goal by reaching the finish line. However, the word, achieve, could also be used here. You could say, "I am on the way to achieving my goal!" To achieve your goal means, not just to complete it but to be successful! If you run a race and have the goal of winning, you achieve your goal when you come in first!

Yes you can! “ After getting out of depression she is on the way to accomplishing her goals.”

Yes you can. You are, I hope, on the way to accomplishing your goals in life.