After the 1.1 update, players will be able to obtain Barbara by reaching Adventure Rank 18 or higher and complete the quest "A Long Shot", which is the final story quest in Mondstadt. Players who obtained Barbara from Barbara's Shining Debut event can still participate and claim her again. The event has no time limit.
Barbara's Shining Debut
This event has ended.
Officially announced through Genshin Impact's Twitter, all players who create an account and reach Adventure Rank 20 before version 1.1 goes live will be able to obtain Barbara via in-game mail! This does not mean that Barbara is a limited time character since you can also get her from the gacha. Be sure to check the official news for when version 1.1 will arrive!