Since in the Steam version the developer can't hide achievements, it's clear *what* they are, see here: http://steamcommunity.com/stats/67370/achievements

The ones without description are the secret achievements.

<strike>I will list them here and update the answer when I know how to unlock them:</strike>

- *Cheque Please!* - I Got this one when I got reunited with fat tony after the subway level. Doesn't seem to be more than a "story achievement"
- *I'm Just Getting Started* - Find and interrogate Swifty
- *Escape the Brotherhood* - Survive the interrogation
- *Storm the Mansion* - Take back your mansion
- *One Flew Over...* - Return to reality...?
- *Sweet Revenge* - Avenge your Aunt Sarah
- *Allies in Strange Places* - Escape the asylum with help from the inside
- *Date Night* - Protect Jenny
- *Back in the Saddle* - Rescue Jackie from the Iron Maiden
- *Step into Hell...* - Defeat Victor