WooCommerce Discounts adds the paratemer products_discounts to the [gamipress_achievement] shortcode which accepts yes and no as value. By default this parameters is setup as yes.

Example:
[gamipress_achievement products_discounts="yes"]

Also, on the GamiPress: Achievement widget will appear the Show Discounts option to let you enable or disable it.

Both methods will output a list of the discounted products as well as the discount amount:

If users earns the achievement, then the output will change noticing the discounts he could expend and in which products:

Also, the price on each product page will be updated showing the new one: