To "aim for" something is to work towards a particular goal.
The goal must be specific for the word "aim" (or "aiming") to have any meaning. Taking aim is as in archery or marksmanship; it is to identify a specific, particular target and aim a weapon at it, preparing to fire. Thus, figuratively, this means to move closer to one goal, rather than many.
Example: U.K. Universities Minister David Willetts urged high school graduates who did not successfully obtain a place at a university (when trying to do so) to do volunteer work to improve their resumes and to consider aiming for heavily attended (high student population), less exclusive, less prestigious universities. This would give students refused entry to better universities an opportunity to get some kind of university education, rather than nothing.