The phrase "achieving a world" is correct and usable in written English.
It can be used when discussing goals or aspirations related to creating or transforming a global situation or environment.
Example: "Our organization is dedicated to achieving a world where everyone has access to clean water and education."
Alternatives: "creating a world" or "building a world".
For that reason, our chances of achieving a world-wide free press appear to us only as good as our chances of achieving a world government.
We are also dedicated to achieving a world without nuclear weapons.
Until very recently, it seemed that television in the UK was on the verge of achieving a world first.
President Assad is the last major roadblock to achieving a world free from the horror of chemical weapons.
Such progress towards achieving a world where no animal has to suffer and die for the sake of cosmetics is encouraging.
His allegiance to the Jewish people is resolute, as is his commitment to achieving a world at peace and in harmony.
Reagan, whose capacious mind could hold many contradictory ideas at once, believed both that the Soviet Union was doomed and that it was on the verge of achieving a world-wide triumph.
From Richard Price, chief exercutive of the Office of Rail Regulation The government's plan for the railways between 2014 and 2019 sets out a massive programme of investment towards achieving a world-class rail service, underlining the importance of rail in economic growth and connectivity across England and Wales.
In a dream start to the year the Briton won silver in the long jump at the World Indoor Championships in March before going on to set a string of personal bests, breaking British records and achieving a world-leading heptathlon score in the prestigious Hypo-Meeting at Gotzis in June.
In May this year we achieved a world record price, selling a late '50s example for $297,000".
That work must truly become our own, if we hope to achieve a world free and equal for all.
