Here are five kakkoii fighting phrases you might hear in anime Japanese or read in manga. Listen for them when you get to the fighting scenes.
Please note, all five of these can be rude--they are, after all, fighting words. Be careful how you use them, but saying them to your close Japanese friends could be fun.
Let's get started with some Anime Fighting Phrases in Japanese...

かかってこい!
Bring it on!
The かかって comes from a word that means "to start," "to deal with," "to handle." こい is a somewhat rude command that means "come on!"

うけてたつ!
I accept your challenge!
When you are ready to take up the gauntlet, say, 「うけてたつ!」

まけるもんか!
I'll never lose!
Said when things are not going well for the bad guy and he is about to lose. もん is an ender used for emphasis. もんか is used for creating rhetorical questions when the speaker actually believes the opposite is true. "Am I about to lose? No way!"

おぼえてろ!
I'll get you for this!
The bad guy is lost and he knows it. He is in an embarrassing retreat, but to save face, he says to the victorious hero, 「おぼえてろ!」 Literally, this is "I'll remember this." It can mean, "You'll be sorry!" or "You'll regret this!" or "I'll get even someday!"

ちくしょう!
Darn!
This is also pronounced ちきしょう. Literally, this means "livestock" or "beast." When said when upset, however, it is a light curse. Dammit! Hang it all! Darn!
Almost tempted to watch anime! Thanks for this. I enjoy them all with internal dialogues.
Thank you! I’m not a big anime fan either, but both Amazon Prime Video and Netflix have a great selection of anime.