Context: Kitano Seiichirou 北野誠一郎 enters the classroom and sees his seat is currently occupied by Takehisa Yuji 竹久優二, who is a delinquent.
komatta naa doushiyou こまったなあ どうしよう
[Oh no]. [What should I do]?
komaru 困る
To trouble. Often used in reference to inconveniences and problems. In this case, someone being seated in his seat "troubled" Seiichirou.
nante ieba kado ga tatanai darou なんていえばカドがたたないだろう
What do [I] say [to solve this amicably], [I wonder]?
kado ga tatsu 角が立つ
(For) corners to stand. (literally.)
When an action makes a relationship worse. In this case, asking Yuji to move to another seat might make him mad.
kuso... bibitte tamaru ka くそ・・・びびってたまるか
[Shit...there's no way I'll chicken out!]
Yuji thinks Seiichirou is challenging him into a stare down.
bibiru びびる
To be afraid. To chicken out. To drop out of a challenge.
tamaru 堪る
To endure. (literally.)
Often used in the patterns tamaru ka and tamaru mono ka to say they won't endure something, that something isn't acceptable.
gan-tsuke nara makenee zo ガンつけなら負けねえぞ
If it's a stare down, [I] won't lose!