This control has several styles in MahApps.Metro:
Default
This is the basic style for the Slider. It applies automatically if you don't use a custom style.
If you want to base your custom style on that style, you need to add BasedOn="{StaticResource MetroSlider}"
FlatSlider
To use that style you need to load resource dictionary
<ResourceDictionary Source="pack://application:,,,/MahApps.Metro;component/Styles/Controls.FlatSlider.xaml" />
and explicitly set the style of the Slider to Style="{DynamicResource FlatSlider}"
This style could be dynamically changed to:
For that you need just to change TickPlacement property from None to any other.