This is a good site to bookmark for helping with addon stuff.
https://warcraft.wiki.gg/wiki/Warcra..._customization
Gethe also keeps a copy of the Blizzard API Code available online at
https://github.com/Gethe/wow-ui-source which many of us utilise to help us. You can also download your own copy following these instructions
https://warcraft.wiki.gg/wiki/Viewin...interface_code.
That said, the following is where you can see the Achievement specific set of functions on the site
https://warcraft.wiki.gg/wiki/World_...I#Achievements
With this one probably being the first one I would try.
https://warcraft.wiki.gg/wiki/API_Ge...ntCriteriaInfo
You will likely have to make sure Blizzard_AchievementUI addon is loaded and available by either setting it up as a required dependency addon in your addons TOC file so that it loads before your addon and testing for
https://warcraft.wiki.gg/wiki/API_C_....IsAddOnLoaded before doing any Achievement related functions.