Accessing an Archived Ambush
Base rules state that the runner accesses all cards in Archives when they access Archives.  When they do, they resolve the effects of the cards normally.  This goes for things like Shock, NAPD Contracts, and Shi.Kyu.  However, text on the card always overrides basic rules in the game.  You can see this with cards like Snare! and Fetal AI where they specifically do not trigger their abilities if they are being accessed from Archives.  However, Fetal DOES still cost the two credits to steal from Archives, as that ability is not suppressed in Archives.

This is why a Jinteki thousand-cuts deck is deadly.  Even if a Shock is trashed, it's still deadly in Archives and will happen every time the Runner tries to access that server.  Another thing to note is that Personal Evolution still happens after the Runner steals any agenda from Archives.

One note on this, however.  Even though the Runner has to access everything if they want it to be considered a successful run, they are allowed to choose the order in which they access these cards.  So, if you would access Archives and steal your final few points, you do not flatline as a result of other cards doing damage to you.  Nice to know when Jinteki starts really burying their agendas in there.