"prospect of achieving" is correct and usable in written English.
You can use it when talking about the possibility of succeeding in a particular activity and the steps needed to reach success. For example, "I'm optimistic about the prospect of achieving my goals by the end of the year."
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.
As the crisis deepens, Syrians face the prospect of achieving neither.
Even though many councils have little prospect of achieving this threshold the number bidding for almo cash is heavily oversubscribed.
But there is no prospect of achieving the breakthroughs we need on climate change, poverty or in other areas without global agreement.
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.
Scientists at a workshop held recently by the Human Genome Project, for instance, discussed the prospects of achieving the "thousand-dollar genome".
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.
