I found this excellent write up on the limitations of attorney-client privilege
The privilege applies only if (1) the
asserted holder of the privilege is or sought to become a client; (2)
the person to whom the communication was made (a) is a member of the
bar of a court, or his subordinate and (b) in connection with this
communication is acting as a lawyer; (3) the communication relates to
a fact of which the attorney was informed (a) by his client (b)
without the presence of strangers (c) for the purpose of securing
primarily either (i) an opinion on law or (ii) legal services or (iii)
assistance in some legal proceeding, and not (d) for the purpose of
committing a crime or tort; and (4) the privilege has been (a) claimed
and (b) not waived by the client."
*Source: United States v. United Shoe Mach. Corp., 89 F. Supp. 357, 358-59 (D. Mass. 1950)
So based on this there could be several things that would apply that would limit the attorney-client privilege.
If the attorney had never represented the "client" and had not entered into some sort of an agreement where the client could reasonable expect that the privilege would be granted. Something to the effect of:
client:I commited a crime and would like you to represent me.
Lawyer: Ok tell me what happened
Here the client clearly indicated he was looking for representation and the attorney indicated he understood and asked for the details. In this case, based on the criteria set out in USvUSMC(quoted above) the privilege would exist.
Now if the client indicates that he left the victim to die, then yes the privelege could be breached due to:
Crime or Fraud Exception. If a client seeks advice from an attorney to
assist with the furtherance of a crime or fraud or the post-commission
concealment of the crime or fraud, then the communication is not
privileged. If, however, the client has completed a crime or fraud and
then seeks the advice of legal counsel, such communications are
privileged unless the client considers covering up the crime or fraud.
The attorney has reasonable belief that a crime is still being committed and allowing the victim to die. In fact if the body had not been found then it could be argued that the failure to report a death crime is ongoing and could breach privilege.
Now if the client barged in, confessed the crime, then asked if the attorney would represent him, the attorney could reasonably state that no privilege exists, and could share the confession with the authorities.