Here is the full list of all 22 Asylamba: Influence achievements.
You have completed the tutorial.
You have completed the first act of the Cardanian campaign.
You have completed the second act of the Cardanian campaign.
You have completed the third act of the Cardanian campaign.
You have completed the fourth act of the Cardanian campaign.
You have completed the first act of the Apheran campaign
You have completed the second act of the Apheran campaign
You have completed the third act of the Apheran campaign
You have completed the Cardanian campaign in Dynast mode.
You have completed the Cardanian campaign in Marshal mode.
You have completed the Cardanian campaign in Steward mode.
You have completed the Cardanian campaign in Emperor mode.
You have completed the Apheran campaign in Dynast mode.
You have completed the Apheran campaign in Marshal mode.
You have completed the Apheran campaign in Steward mode.
You have completed the Apheran campaign in Emperor mode.
You have completed Influence in Noble mode.
You have completed Influence in Dynast mode.
You have completed Influence in Marshal mode.
You have completed Influence in Steward mode.
You have completed Influence in Emperor mode.
You were lucky.