moment by moment; hour by hour; with every passing moment
Emphasizes continuous, often dramatic change as time passes. Used adverbially, often with verbs of change or approach.
The situation is changing moment by moment.
The deadline is approaching with every passing moment.
徐々に describes a calm, unhurried gradual change, while 刻一刻と conveys a more dramatic, ticking-clock sense of time passing.
日増しに means 'day by day' and is used for changes measured in days, whereas 刻一刻と can describe change happening even minute by minute.
Reduplication of 刻 (こく, 'moment' or 'time') with the adverbial particle と, literally 'moment by moment'.