I know its Haram to al-Ghibah (backbiting) (talking bad about other people) as there is a Hadith on this. However, does this ruling apply only to backbiting Muslims? Can we talk bad about non-Muslims?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

As you mentioned, backbiting is completely forbidden in Islam. It is one of the great major sins.

Allah Says (what means): {And do not spy or backbite each other. Would one of you like to eat the flesh of his brother when dead? You would detest it. And fear Allah; indeed, Allah is Accepting of repentance and Merciful.} [Quran 49: 12]

The above-mentioned ruling is confined to Muslims.

As for non-Muslims and criminals who demonstrate their misdeeds and corruption, it is not forbidden to backbite them; i.e., to mention their bad deeds.

Ibn Hurmuz said: “I heard the Prophet's () companions cursing disbelievers in Ramadan.” [Maalik in al-Muwatta’]

‘Aa’ishah narrated that a man asked permission to see the Prophet who said: “Give him permission. What a bad chieftain of a tribe he is.” [Al-Bukhari and Muslim]

However, if cursing non-Muslims and criminals leads to harm, sin or making them curse Allah, His Messenger or Islam, then it is forbidden to curse them since such an action, according to al-Qurtubi, will be a means that will lead to sins and misdeeds. So, we are to avoid such cursing to make them avoid doing so against us. Allah Says (what means): {And do not insult those they invoke other than Allah, lest they insult Allah in enmity without knowledge.} [Quran 6: 108]

Allah knows best.