Short answer : I would rule that you get exactly one attack of opportunity, and it must be with your shield.
Reasoning : The below text in the Combat Chapter, under Attacks of Opportunity seems to be saying a given action should only provoke once.
This feat does not let you make more than one attack for a given opportunity, but if the same opponent provokes two attacks of opportunity from you, you could make two separate attacks of opportunity (since each one represents a different opportunity).
Deadly Dodge says, in part
During this time, whenever a creature misses on a melee attack against you, it provokes an attack of opportunity from you.
Mythic Shield Master says
if a foe in reach makes an attack against you and misses by 5 or more that foe provokes an attack of opportunity from you. If a foe attempts to make a combat maneuver targeting your shield (such as sunder) and after the maneuver is resolved your shield is still in hand and not broken or destroyed, that foe provokes an attack of opportunity from you.
In both cases, the thing provoking the AoO is missing an attack against you. The conditions for Shield Master include missing by 5 or more, but it’s still the miss of the attack that is the trigger. Therefore, I see this as just one oppotunity, not two.
If you were missed by less than 5, you would be able to make the AoO in any way you wished.