Hi, Mithli,
I don't think that A G IN inside a girl's name will work. The girl's name would have to be IMARY, but this isn't listed in Chambers in the Some First Names section nor as a main word. I see from a baby names website that IMARY is actually a girl's name, but it is very uncommon. Anyway, if you use "embraced" (or strictly "embraced by") as a synonym for IN, you can't also use it to signify that letters are contained in a girl's name. Similarly, if you were to say that A G IN is contained just in MARY, then you have used the "One" to refer to A and can't also use it to refer to the initial I.
Parsing the clue as "One" = I and then "girl embraced by another" as GINA contained in MARY gives a valid synonym for "fantastic", so I agree that this must be the explanation of the clue.