What was wrong with a "be bolder"/"be more assertive"/"don't be afraid of taking credit for your work"?
I don't see those as useful since it doesn't provide the person any actual guidance or reference point. What does assertive mean? What should I exactly do? How do I do it? "Act like X" provides a well known reference point that they can use to adjust their behavior based on. They can remember all the times they've seen X do something in a similar situation and then just act like that.
If you want to make it super explicit, come up with examples. "Be bolder, for example for this project I saw you doing 80% of the work, you should get to headline the presentation and have top billing on the authors page".
"Act like X" is also potentially useful, if you make it explicit. Explicit is not "Act like a white man" (whaaaa?). Explicit: is "Act like Bob, for example do you remember when HR said he couldn't have a new screen and he insisted"?
It's just an extension of the classic "show, don't tell".
"Be bolder" is different than "what do you think a bold person would do?"
I have had many conversations with people going through a tough time and unsure of what to do or how to feel in a situation and there is this trick to getting people to think differently that almost always works... ask the question
"What would a reasonable person do in your situation?"
Suddenly the person having trouble coming up with the answer "What should I do?" has a perfect answer to "What would a reasonable person do?"
It's a psychological trick that goes after how one thinks about one's self and how one thinks about someone else being quite different. If you refocus your attention to view yourself from an external objective, you often end up with much better judgement.