Changing Hyperlink foreground without losing hover color

Setting the Foreground directly (as you've done) doesn't work, and setting it in a Style doesn't work either, unless you "derive" that style from the default Hyperlink style (which must include the OnMouseOver trigger). So this works:

<TextBlock>
    <Hyperlink>
        <Hyperlink.Style>
            <Style TargetType="Hyperlink"
                   BasedOn="{StaticResource {x:Type Hyperlink}}">
                <Setter Property="Foreground" Value="#0C0"/>
            </Style>
        </Hyperlink.Style>
        Mark as done
    </Hyperlink>
</TextBlock>

Extracting that style back into the Window resources and referencing it with a key would probably make for more-readable XAML, but the above code does the job.

You should build your Hyperlink like this

<TextBlock Width="Auto" HorizontalAlignment="Center">
    <Hyperlink Click="ForgotPassword_Clicked">
        <TextBlock Text="Forgot Password?"/>
    </Hyperlink>
</TextBlock>

And then this style should work for you

<Style TargetType="{x:Type Hyperlink}">
        <Setter Property="FocusVisualStyle" Value="{x:Null}"/>
        <Setter Property="Foreground" Value="Blue" />
        <Setter Property="TextBlock.TextDecorations" Value="{x:Null}" />
        <Style.Triggers>
            <Trigger Property="IsMouseOver" Value="True">
                <Setter Property="Foreground" Value="Red" />
                <Setter Property="TextBlock.TextDecorations" Value="Underline" />
            </Trigger>
        </Style.Triggers>
    </Style>