I agree with you, however one would only use "we are looking at the possibility of achieving..." if one was talking about a plan that may or may not work. However "looking to achieve..." Is simply talking about the goal "Our aim is to achieve..." is synonymous with "looking to" but not synonymous with "looking at the possiblility of..." And as this thread is about "looking to" then really we shouldn't be suggesting other possible phrases that won't convey the correct meaning of the original phrase.
Oh, and "we are looking at the possiblility of" does not mean "We are looking forward to" though both sentences are grammatically correct. And,sorry to contradict almost everything you said, I would say the first sentence is the least confident, as if one is anticipating many things going wrong with your plan to achieve the goal.