Manage and achieve all means successed in doing sth, but manage stresses that you must go through many difficulties before you successed

"I managed to reach the top of Mount Everest" "I achieved my goal of climbing Mount Everest" In the first case, the form is : to manage to + verb In the second case, the form is : to achieve + noun Common nouns to use with "to achieve" are : success, goal, aim, recognition, victory. You can use "to manage to" with all sorts of verbs naturally.