The sentence "achieve justice" is correct and usable in written English. You can use this phrase when you are making an argument for a particular course of action in order to promote fairness or rectify an injustice. For example, "We must take a stand to achieve justice for all people in our society.".
What else can we do to redesign our system and achieve justice, increase public safety and transform lives?
We are there to achieve justice".
There are other ways to achieve justice.
That's the goal of my life – to achieve justice.
"We will achieve justice in this case," Jordan said.
"The usual focus is on fairness: To achieve justice, we need to give women equal opportunities.
One fears that the goal will simply be to accumulate hours and not to achieve justice.
Being a terminologist, I care about word choice. Ludwig simply helps me pick the best words for any translation. Five stars!
Maria Pia Montoro
Terminologist and Q/A Analyst @ Translation Centre for the Bodies of the European Union