Hour by hour, day by day, month by month, year by year, decade by decade, century by century, millennia by millennia…
Myriad by myriad, eon by eon
Infinity by infinity.
(I’m sure there’s a real answer😉)
To Infinity and beyond!
aeon by aeon.
Age by age
…eternity by eternity
Shouldn’t this be “millennium by millennium” ?
I think you are correct for this (the best kind of pedantry ).
While we’re being pedantic …
It’s reasonable for the OP to ask us to continue the sentence. Because of the way numbers work we’ll never finish it. 
+1 to whatever anyone else posts.
Do I win the thread? 
You’re right. Good catch!
…etc.
…this is some bullshit.
To Hell and back?
Kalpa by kalpa.
If I remember this concept correctly, a kalpa is the length of time it takes for a condor flapping its wings to gently brush a mountain over and over every day until the mountain is ground to dust.
Or as wiki puts it
Cyclic day of Brahma in Hindu cosmology lasting 1,000 Yuga Cycles containing 14 Manvantaras and 15 Sandhyās. It is followed by a night (pralaya) of equal length, forming one 24-hour day of Brahma’s 100 360-day years.
Hope you’re taking notes.
Interesting. The bird barely touching something enormous (like a mountain) and grinding it to dust is a parable (usually about the nature of eternity) I have seen often in many forms but I never knew someone coined a word counting it as an increment of time. Cool. Another to add to the list of weird measurements.
Au contraire.
To be even more pedantic, as it stands now, it’s not a sentence, finished or otherwise. It has neither a subject nor a verb.
Ergo, I propose:
Hour by hour, day by day, month by month, year by year, decade by decade, century by century, millennia by millennia, I am getting better and better.
Now it’s a finished sentence. 
…slowly I turned, step by step, inch by inch…