You can export your manga list from MyAnimeList as an XML file and then import it directly into MangaTime.
Follow these simple steps:
Open MyAnimeList and log in to your account.
Then navigate to http://myanimelist.net/panel.php?go=export
Select Manga List from the dropdown
Tap on Export My List
MyAnimeList will generate and download an XML file containing all your manga entries
Go back to MangaTime
Open the Profile tab using the bottom navigation bar
Open up the Settings page by tapping on the gear icon in the top right corner
Press on Import from MyAnimeList and select the XML File tab
Tap on Select XML File and pick the downloaded file from your downloads
Then press on Start Import, wait a few seconds (based on how big your library is) and TADAAA 🎉