親父 means “Dad” usually used by men in casual speech. It’s the same meaning as お父さん but 親父 sounds like you’re more close and equal to your dad whereas お父さん sounds more respectful and it’s commonly used when you are a child. So 親父 is usually used once you have grown up.
ぶたれた is the past tense of ぶたれる which is the passive form of ぶつ meaning “to hit someone”. “A hits B” is “AはBをぶつ” and with the passive form it becomes “B is hit by A” = “BはAにぶたれる”. So this A falls on 親父 and the B is Amuro which is just omitted because it’s clear that Amuro is talking about himself. So 親父にぶたれる means “I am hit by my dad”.
Verb past tense and ことない or ことがない means “have never done before” or “have no experience”. So if you put ある instead of ない it means “have done before” or “have experienced”. So 親父にぶたれたことない means “I have never been hit by my dad”.
も: Many of you already know that you use も as an inclusive particle meaning “also” or “too”. for example, わたしも行く “I will go too” これもほしい “I want this too”. But this も means “even” which emphasises what comes before. Amuro also said “２度もぶった” meaning “You hit me TWICE!”. This も emphasises the quantity “twice”.
のに is a conjunction meaning “even though”. For example, たくさん寝たのに、まだ眠い (Even though I slept a lot, I’m still sleepy). It’s used when what is stated in the second clause goes against what is expected from the first clause. It implies unexpectedness or dissatisfaction, and it’s often used for complaint. But by dropping the second clause and finishing the sentence with のに you can express your feeling of discontent even stronger.