"prospects of achieving" is correct and usable in written English.
You can use it when referring to the possibility of reaching a desired outcome, for example: "The prospects of achieving success in this venture appear to be quite high."
Cameron says he is "optimistic and confident" about the prospects of achieving change.
Herbert now had good prospects of achieving high public office, if he so wished.
In his remarks Monday, Mr. Rehn stayed upbeat about Ireland's prospects of achieving projected growth of 1.9 percent in 2012.
Palestinian moderates will be strengthened to confront the militants only when there are real prospects of achieving a satisfactory political solution to this problem.
Scientists at a workshop held recently by the Human Genome Project, for instance, discussed the prospects of achieving the "thousand-dollar genome".
Furthermore, professors' prospects of achieving tenure at their own institutions or of being headhunted by others are themselves linked to their publication in journals.
Here, we describe recent advances in overexpression of multi-subunit membrane protein complexes, the strategies to stabilize these complexes and highlight major achievements in membrane protein structural research that were facilitated by the prospect of achieving subnanometer to near-atomic resolution by electron cryo-microscopy.
Two months on, the prospect of achieving these goals is under threat.
The political division between the territories has muddied the prospect of achieving a Palestinian state.
Does the prospect of achieving true mastery in that line of work excite you?
As the crisis deepens, Syrians face the prospect of achieving neither.
