一気(いっき)

喉(のど)が渇(かわ)いていたので一気(いっき)に水(みず)を飲(の)みました。

I was thirsty, so I chugged the water all at once. {chug!, drink! (said repeatedly as a party cheer)}

締(し)め切(き)りを目前(もくぜん)にした画家(がか)は作品(さくひん)を一気(いっき)に仕上(しあ)げた。

The translation does not correspond with the given definitions (chug!, drink! (said repeatedly as a party cheer)). The correct translation would be: "The painter, with the deadline looming, finished the work all at once." {chug!, drink! (said repeatedly as a party cheer)}

内容(ないよう)が面白(おもしろ)かったから一気(いっき)に漫画(まんが)を読(よ)み切(き)ってしまった。

Since the content was so interesting, I ended up binge-reading the entire manga. The party cheer definitions provided do not fit in the context of this sentence. {chug!, drink! (said repeatedly as a party cheer)}

親友(しんゆう)の拓真(たくま)はコーラを一気(いっき)に飲(の)み干(ほ)すなり盛大(せいだい)にゲップをしました。

My best friend Takuma chugged his cola and let out a huge belch. {chug!, drink! (said repeatedly as a party cheer)}

丘(おか)を一気(いっき)に駆(か)け下(お)りたら心拍(しんぱく)数(すう)が一気(いっき)に普段(ふだん)の三(さん)倍(ばい)程(ほど)に上(あ)がってしまいました。

The translation does not seem to relate to the provided definitions. However, the accurate translation for the sentence would be: "When I ran down the hill all at once, my heart rate soared to about three times its usual rate." {chug!, drink! (said repeatedly as a party cheer)}