The Html.ActionLink helper HTML encodes the link text which prevents you from embedding HTML in the link text.
For this same reason you cannot use Html.ActionLink and pass in an tag to make an image a hyperlink.
For basic styling of a link, I'd recommend using one of the Html.ActionLink overloads to specify a CSS style via the anonymous object syntax like so...
@Html.ActionLink("Please Edit Me", "Edit", null, new { style="font-weight:bold;" })
Unfortunately, that applies bold to the entire text of the hyperlink when what you're wanting is just the word Edit to be bold. In which case I would do this...
<a href="@Url.Action("Edit")">Please <b>Edit</b> Me</a>
... or this ...
<a href="@Url.Action("Edit")">Please <span style="font-weight:bold;">Edit</span> Me</a>
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