What counts towards ascension achievements? (Cookie Clicker)

I've been farming for the Reincarnation achievement, but I want to be sure what counts as an ascension. Do I need to gain prestige every run, or can I just spam-click the Legacy button?

Solution 1:

According to the wiki, you have to gain at least one prestige level each run to count towards this achievement.

This can be done pretty quickly by swapping between clicking the "buy all" button for upgrades and buying the maximum amount of the most expensive building you can buy. Make sure that you have upgrades in your Permanent Upgrade Slot heavenly upgrades that will increase your cps by the most under low optimization, such as kittens and upgrades that double the output of the most expensive building.