How does the United Nations gain achievement?

I think you are either asking how the United Nations came into being or how it achieves its objectives. In terms of how it achieves its objectives, it does so through consensus at the United Nations General Assembly where member states vote on initiatives, referendums, and other international legislation. However, the legislation only works if member states go along with it.
In terms of how the United Nations came into being, it was founded after WWII as a way to ensure that global war could be avoided in the future. Its precursor, the League of Nations, was similar in nature but failed to attract countries such as the US that saw it as limiting national sovereignty. The UN includes a Security Council made up (largely) of the victors of WWII: the US, France, Russia (formerly the USSR), China, and UK. The Security Council deals with the most serious international incidents. The Security Council also has a revolving member state made up of any of the other nations to ensure that the regular five do not dominate the Council's agenda.
Working with the UN are also a number of autonomous organizations ranging from UNESCO to the World Health Organization. Their collective mission is to further goals that affect the entire planet, not just individual countries. However, the UN does have its critics who believe that the highly politicized efforts by the organization are to create a one-world government and limit the freedoms of smaller countries. Even larger countries such as the US sometimes rebuke UN legislation that curtails on their sovereignty—the most recent example being the Paris Climate Accord, which the US pulled out of in 2017.
https://www.theguardian.com/world/2015/sep/07/what-has-the-un-achieved-united-nations

https://www.thoughtco.com/the-united-nations-p2-1435441