"despite various efforts" is correct and usable in written English.
It is typically used to indicate that despite multiple attempts or actions, something remains unchanged or has not been successful. Example: Despite various efforts to fix the leak, water continued to drip from the pipes.
This week in 1922, the Supreme Court unanimously ruled that the amendment was valid despite various efforts to discredit it.
Despite various efforts to form pan-Asian coalitions, many Asian immigrants identify themselves chiefly by country of origin and socialize in their native languages.
Despite various efforts, including the expansion of Pell Grants and the forgiveness of some federal loans, student debt surpassed $1 trillion by 2015.
Despite various efforts by later thinkers to fuse the problems of kalām with those of philosophy (and mysticism), theology preserved its relative independence from philosophy and other nonreligious sciences.
Despite various efforts to shed light on the different aspects of repair and maintenance processes, our entire understanding of the repair practices done on consumer electronics comes from either the manufactures or professional repair experts.
3, 13 NSAID gastropathy remains a silent threat, despite various efforts to manage it.
The patient, however, manifested cardiac arrest despite various effort of fluid resuscitation.
This graphic provided by Twitter clearly illustrates the problem: the company — despite its various efforts — has hardly moved in the last quarter, and excepting Q4 has had nearly identical quarters for the last year.
However, despite these various efforts, clinical gains have been modest.
Despite the various efforts aiming at ensuring that communities participate in deciding about their affairs including health issues, operationalization of such efforts is poorly done.
But if the hero of The Impressionist is hollow despite all his various efforts at assimilation, it isn't because he is a copy, but because he is copying people who are hollow already.
