Do Catholics believe that Mary is the co-savior of the world?

No. The Catholic Church teaches that Jesus Christ is the one savior of the world.
You will sometimes hear people say that Catholics believe that Mary is the “co-redemptrix.” There is a lot of misinformation around that, so here’s a quick explanation.
Over the last several years, many Catholics around the world have signed petitions urging the Pope to make a dogmatic declaration that Mary is the “co-redemptrix.” They feel that this title will emphasize the unique and irreplaceable role that Mary played in the salvation of the world: namely, conceiving, giving birth to, and supporting Jesus in his mission. They do clarify (correctly) that she is subordinate to her Son, and that Jesus is the one and only Redeemer. So when they say “co-“, they don’t mean “on equal footing with”; rather, they mean that she played a unique part in helping Jesus do his work of salvation.
What they say here is, in fact, nothing new. The Church has consistently taught that as the mother of Jesus, Mary did play a very unique and essential role in bringing the Savior into the world. At Vatican II, the Dogmatic Constitution on the Church affirmed as much, saying, “[Mary] conceived, brought forth and nourished Christ. She presented Him to the father in the temple, and was united with him by compassion as he died on the cross. In this singular way she cooperated by her obedience, faith, hope and burning charity in the work of the Savior in giving back supernatural life to souls.” ( Lumen Gentium 61; italics mine). In other words, no one else played the part that she did in bringing Christ into the world so he could save us. At the same time, the Church teaches that she is always subordinate to her son. As the Dogmatic Constiuation on the Church states a few lines later, “No creature could ever be counted as equal with the incarnate Word and Redeemer.” (Lumen Gentium 62)
What is problematic to many both inside and outside the Church is that the very title “co-redemptrix” invites misunderstanding. It seems to put Mary on the same level as Christ (she isn’t), and seems to imply that she is divine (she isn’t). Those who are critical of the title also worry about its impact on ecumenical efforts with other Christian churches.
And in spite of the petitions signed by those who support the title of co-redemptrix, no pope has ever made a dogmatic declaration to formalize the title and make it official.