Arch Enemy
Formidable Adversary, Great Enemy
noun
Your big enemy is your worst enemy. Your arch enemy.
大敵 is for a powerful or dangerous opponent, whether it's a formidable adversary in battle or competition, or something abstract, like calling carelessness your great enemy.
This is a jukugo word, which usually means on'yomi readings from the kanji. Both kanji have a couple different on'yomi readings though, so here's a mnemonic to help you remember which ones to pick:
Your arch enemy is the tie techie (たいてき). Who's the tie techie? He's the tech support guy at work who always wears the same tie and never helps you. He just says "try restarting your computer" to every problem, which isn't helpful. He's not just a great enemy, he's basically your nemesis. You hate that tie techie.
ワニカニの大敵はだれだと思いますか？
Who do you think is Wanikani's rival?
オレたちの大敵が、ついに敗北を認めたぞ。
Our arch enemy finally acknowledged their defeat.
分かっていると思うけど、油断大敵だよ。「サルも木から落ちる」って言うだろう？
As you all know, carelessness is man's greatest enemy. People say "even monkeys fall from trees," right?