Most people describe call what you're describing 'ambition.' Some people want to do more than other people and set loftier goals for themselves. However, I think it's a huge mistake to say that "in these cases actually achieving, eventually leads to a feeling of happiness." You're implying that ambition is the only road to happiness, when there is a preponderance of evidence to the contrary.

I think it's far more likely that highly ambitious people have a far more difficult time being as happy as other, "normal" people. If you spend a lot of mental energy focusing on the points where the world rubs you the wrong way you're not going to feel happy regardless of whether you try to fix those points.

I'm not saying that ambition is the only road to happiness.

I think you're correct - more highly ambitious people probably do have a far more difficult time being 'happy'.

I am trying to imply that the pursuit of happiness can make people work harder. For the ambitious - it's often used as a metaphorical carrot on a stick.