"may achieve that" is a perfectly correct and usable phrase in written English.
It can generally be used any time when you wish to express the idea of working towards a goal or desired result. For example, "If we work hard, we may achieve that promotion we've been aiming for."
Stern may achieve that goal someday, but she hasn't this time.
Oddly, by pushing so hard, Mr. Bush may achieve that which seemed impossible: unity among Iraq's disparate ethnic and political groups.
The court decisions may achieve that result, but in a way the critics dislike.If anything, the judges seem to have prodded the government into a firmer line.
On Sept. 22, after a nine-year pursuit, he reported a finding that may explain exactly how very low calorie diets -- the one intervention known to prolong life in experimental organisms -- may achieve that end.
Third place will secure a Europa League qualifying spot next season but the Highlanders may achieve that through the cup and thus send the fourth-placed side into Europe as well.
However, if Israel continues to go down its present very narrow and rigid definition of security it may achieve that particular ambition, but at the expense of all of those other crucial interests, needs, and goals of the Zionist project.
He may or may not achieve that goal.
The bills now in Congress, however, may not achieve that end.
And Mr. Maxwell (who'da thunk it?) has provided a lovely, resourceful and unexpected coup de th?re that suggests that, yes, flat lives may sometimes achieve that longed-for third dimension.
Further analysis may yet achieve that, but team members expect no further help from their instruments on Mars.
"I may not achieve that challenge in six-ten weeks but, going forward, if I'm coaching Scotland, I've got to understand the Scottish way".
