"first eventually" is correct and usable in written English.
You can use it when you want to emphasize the order of occurrence of two events or objects. For example: "I put on my shoes first, and then my jacket eventually."
But the piping falsetto, funny at first, eventually palls as Lucidus's travails grind on.
They used rudimentary tape recorders at first, eventually acquiring professional equipment that allowed for studio tricks like overdubbing and slapback echo, which led to stranger, deeper sounds.
The singers remain seated at first; eventually the couples stand and move around the room (or out of it), each enacting a sequence of fights, breakups and reconciliations.
She found Oxford intimidating at first, eventually building up the courage to audition for a play – A Midsummer Night's Dream again.
But Mr. Paterson gradually alters each line, having each take on characteristics of the others at first, eventually softening the edges to create a tightly knit (if not quite homogenous) dreamlike wash.
The venture quickly thrived, and after several months she closed the business and invested some of her earnings into trading commodities, modestly at first, eventually on larger and larger a scale.
The cute-at-first, eventually annoying coati — aardvark-like mammals that are extremely good at stealing your food — are everywhere.
The fourth eventually resulted in a mistrial.
Andy Murray, seeded fourth, eventually broke clear of Richard Gasquet, 4-6, 6-4 (5), 6-1, 6-1, 6-1.
Phelps and the Eighth eventually followed with the rest of the Army of the Potomac.
But Hughes was not as sharp in the seventh, eventually loading the bases and getting just one out.
