Global biodiversity is facing unprecedented pressures, calling into question the effectiveness of existing governance systems aimed at halting extinctions. Renewed hope arose with the recent Conference of the Parties (COP) to the Convention on Biological Diversity (COP15 December 2022) and the Convention on International Trade in Endangered Species (COP19 November 2022). Yet, barriers remain that hamper biodiversity conservation. Identifying and overcoming these barriers is crucial for success. We considered previous lessons learned to show that current barriers to conservation are centered on a multidimensional array of mismatches among legal (law), ecological (science), and sociocultural (human) dimensions across the short, medium, and long term. Focusing on highly migratory marine megafauna (whales, sharks, and turtles), we used the Rubik's cube as a metaphor to conceptualize the multidimensional mismatches and devised a pathway for solutions that is highly dependent on strict alignment across all dimensions. We recommend the continuous cycling across all dimension interfaces to align the use (and update) of regulations and processes in law, improve data and experimentation methods in science, and develop education and engagement actions in the human dimension. This timely alignment across all dimensions is key to achieving biodiversity targets and avoiding further extinctions.