"to accomplish this goal" is correct and usable in written English. You can use it when you want to emphasize an overall goal that you are trying to achieve. For example, "We need to come up with an effective strategy to accomplish this goal within the next three months.".
To accomplish this goal, he helped forge our trade association.
We are disappointed that a chance may be lost to accomplish this goal".
Instead of pen and paper, the internet's founders used technology standards to accomplish this goal.
Initially, there was considerable debate within the Bush administration about how to accomplish this goal.
Collective bargaining in the private and public sectors is a very good way to accomplish this goal.
To accomplish this goal, we used two data sets.
To accomplish this goal we conducted two follow-up analyses.
Thanks to Ludwig my first paper got accepted! The editor wrote me that my manuscript was well-written
Listya Utami K.
PhD Student in Biology, Bandung Institute of Technology, Indonesia