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俺が大学生の頃、バイトがあまりに嫌でブッチしようとしたら親父に
→ “Back when I was a college student, I hated my part-time job so much that when I tried to quit, my dad...”
俺 ore = I (masculine, informal pronoun)
が ga = subject marker particle
大学生 daigakusei = university student (n.)
大 dai = big / large
学 gaku = study / learning
生 sei = life / born
の no = possessive/genitive particle ('s) or 'of'
頃 koro = time / period / around the time that
、 = comma (punctuation)
バイト baito = part-time job (loanword from English 'part-time')
が ga = subject marker particle
あまりに amari ni = so much / extremely (adverbial phrase)
あまり amari = not much / little
に ni = intensity particle (makes 'amari' an adverb meaning 'to an extreme degree')
嫌 iya = hate / dislike /讨厌 (na-adjective)
で de = causative/resultative particle ('because of', 'so much so that')
ブッチ buchii = quit / break off (slang, onomatopoeia for cutting something off abruptly)
しよう shiyou = try to do / attempt (volitional form of 'suru')
し shi = do (stem of 'suru')
よう you = let's / try to (volitional auxiliary)
と to = quotational particle ('thought/said')
したら shitara = when I did / if I did (conditional form of 'suru')
し shi = do (stem of 'suru')
たら tara = if / when (conditional suffix)
親父 oyaji = dad / father (colloquial)
に ni = target/direction particle ('at/to'), indicating who received the action