Does anyone enter Paradise by their deeds regardless of their faith, or is entering Paradise linked to faith?

Paradise is entered only by believers, as per the Hadith: "None shall enter Paradise except a believer." The man who gave water to the dog was a Muslim, and the woman who imprisoned the cat was not mentioned as having entered Paradise. Ibn Hajar reported from Iyad that she was a disbeliever, and Ibn Hajar supported this view.