The phrase "a way that achieves" is correct and usable in written English.
You can use it when describing a method or approach that successfully reaches a desired outcome or goal.
Example: "We need to find a way that achieves our objectives while staying within budget."
Alternatives: "a method that accomplishes" or "an approach that fulfills".
The encounter of the oral history interview brings together the past and the present in a way that achieves catharsis and resolve, rather than some contrived moral clarity.
Possibly the most interesting sandwiches in the world, Mexican tortas combine boldly seasoned elements in a way that achieves both complexity and a certain delicacy.
A "system" is an interconnected set of elements coherently organised in a way that achieves something.
We are working with the industry to develop this proposal in a way that achieves that objective".
You can never go home again, but you can identify what it was that you liked about your home and maintain those presences in your current life in a way that achieves an almost totally satisfying approximation.
Each component deal presents a tactical challenge, but sequencing the parts in a way that achieves the target outcome is a strategic challenge that can unfold over months or years.
Managers must be able to apply creative thinking in a systematic way that achieves results: revenue growth, delighted customers, a stronger community or some other measure of impact.
Doctors know all about probabilities and trade-offs, but we don't know much about how to engage patients in decision-making in a way that actually achieves the most desired long-term outcome.
It's OK to have high expectations for a relationship if they're achievable and you're prepared to behave in a way that can achieve them.
We were not confident in our ability to manage the project in a way that would achieve our investor's goals.
The budgets allowed me to have a spending plan and structure it in a way that helped achieve my goals.
