If your convinced the may update was the reason for the fall then research what the may update targeted. Then once you understand you are then armed with the knowledge to address the issue.
It can often be overlooked that an update favours the sites that overtook you because they have done something better and its not something you have done wrong as such.
You may get advice to build more backlinks but ignore them. Do your research, find the issue and fix it. That is the correct and only way to solve issues like this.