The Plan:
The main part of the plan is to launch a tactical air strike against the impending threat. If we cripple them with one fell swoop, then the Penguins will be neutralized.

.
The strike teams would have to launch from Tasmania, South Africa,
and southern Chile or Argentina to ensure a quick strike.

While the nuclear strike is underway, a series of sniper teams will be set up throughout the zoos in the world to take out the Penguin spies.

Unfortunately, to avoid suspicion from the penguins, the research teams that would be on the job at the time will not be informed. A barbeque and memorial service will held in honor of these lost scientists a soon after the Penguin threat is eliminated.