This is the 1370th most frequent Japanese word.
一気に
"All at once" or "in one go."
In this sentence, "一気に" is used to describe the action of quickly running up the hill without pausing.
彼は坂を一気に駆け上がった。
He ran up the hill in one go.
Here, "一気に" conveys the idea of completing the solving of issues in a single continuous effort.
一気に問題を解いてしまおう！
Let's quickly solve all the problems at once!
This usage of "一気に" emphasizes the sequential and immediate action of drinking all at once.