First you need to set up 2 step verification:
Login to your Gmail account and go to settings (the cogwheel on the right)
Then to all settings
There see 2 step verification.
Follow the steps to set that up.
Then Login again to your Gmail account by going to manage my account and to security on the left.
Then go to Google app password and generate a password.
Copy the password and save it wherever you save passwords.
Open Eudora and tap on special and ask it to forget the password for your Gmail account.
Then check mail and it will ask for a password.
Paste the Google app password and tick the remember password box.
Hope it works for you.