For Mark character needs 20 upgrades. One of my players plays pirate prince who aligned with Slaanesh and has many basic slaanesh upgrades (skills, talents, stats). How these upgrades count towards Mark?

By RAW, Skills and Talents that are part of an Archetype or Race does not count towards Alignment, since they are not Advancements.

Hm. Seems that Archetype of Slaanesh has a problems with acquiring Slaanesh Mark.

The forum work around for this and staying aligned come the next corruption check is to declare the starting character to be 5/0/0/0 on advancements. That way he won't unalign when he gains corruption unless he buys non slaneesh talents. This way he'll need 15 advancements rather than 20 more to get the mark.

Definitely something they should have commented on with the archetypes.