In order to be able to translate the difference between these two terms it is necessary to understand the distinction between "in deed" and "in fact" which could be accomplished by contrasting
Something that is done, performed, or accomplished; an act:
Do a good deed every day.
something that actually exists; reality; truth:
Your fears have no basis in fact.
"Deed" in Spanish would be "acción", while "fact" would be "hecho". So, when you prove something "in deed", you would be proving it with deeds (actions), when you prove something "in fact", you would be proving it with facts.
"In fact" could be translated as "en/con/de hecho" while "In deed" could be translated as "en/con/de acción/obra". So, a Spanish equivalent to "prove it in deed" would be "pruébalo con acciones/obras" and an equivalent to "prove it in fact" would be "pruébalo con hechos".
Very common translations of the use "She is beautiful, in fact" (and "She is beautiful, indeed") are:
- Ella es bella, de hecho
- Ella es bella, ciertamente
- Ella es bella, en verdad
- Ella es bella, en realidad
- Ella es bella, en efecto
- Ella es bella, verdaderamente
- Ella es bella, realmente
- Ella es bella, efectivamente
Now, it makes more sense in Spanish to phrase these translations a little differently:
- De hecho, ella es bella
- Ciertamente, ella es bella
- En verdad, ella es bella
- En realidad, ella es bella
- En efecto, ella es bella
- Verdaderamente, ella es bella
- Realmente, ella es bella
- Efectivamente, ella es bella
Regarding "She is beautiful in deed" the translations would be a little different:
- Ella es bella por sus acciones/obras
- Ella es bella con sus acciones/obras
- Sus acciones/obras la hacen bella (her deeds make her beautiful)
- Sus acciones/obras la embellecen (her deeds make her beautiful)
So, the closest in Spanish would be to make a reference of the impact of the deed in a particular context. (Her deeds make her beautiful).
Curiously, the closest there is to an example of this concept in native Spanish is the following phrase:
Los hijos y los maridos, por sus obras son queridos.
Which would be similar to "The children and husbands are loved by their deeds".
An example from the previously mentioned strategy to translate this concept by alluring to the deeds can be found in another native Spanish phrase:
Sus obras la enaltecen.
Which would be roughly similar to: "Her deeds upraise her", referring to the impact of her deeds have on her character.
Please keep in mind that not all concepts in a particular language have an exact equivalent in all other languages. So, sometimes some compromises have to be made in order to communicate a particular idea.
Finally, consider the link provided to the subtle difference between "in deed" and "in fact":
Actually, indeed comes from a shortening of 'in deed'. This was when 'in deed' was similar in usage to 'in fact'. Over time, the meaning of deed has evolved I guess, hence the difference.
This particular comment sheds some light on how "in deed" might have become "indeed". If that is the case, then the options given for "indeed" should suffice when looking for a suitable translation. If you still feel that there is a more noticeable difference between "in fact" and "in deed", please update your question and provide further examples that help native Spanish speakers understand the subtle distinction between the two.