Do citizens of the Philippines need a visa to visit South Korea?

As stated by Timatic, the database used by airlines:

Visa required, except for Nationals of Philippines with a residence permit issued by Australia if in transit through Korea (Rep.), holding confirmed onward tickets on flights departing within 30 days, when:

-arriving from Australia, departing to a third country (e.g. SYD-ICN-PVG); or

-arriving from a third country, departing to Australia (e.g. PVG-ICN-SYD); or

-arriving from a third country after having transited that country for a maximum stay of 3 days, departing to Australia (e.g. PVG-SGN-ICN-SYD); or

-arriving from a third country, traveling to another country and staying there for a maximum stay of 3 days, then departing to Australia (e.g. PVG-ICN-SGN-SYD).

So if you don't fly direct in both directions, but make a stopover at least in one direction, you do not need a visa for max 30 days.

Otherwise, you do need a visa

Your passport is what matters, so unless you have Official/Diplomat passport, you will need to apply for Tourist visa.

Korea Immigration Service Visa Navigator

Settings: Asia>Philippines>Short Term Visit>90 days or less

Visa Exempted(B-1): A person with a diplomatic or official passport of Philippines can visit Korea without a visa and stay for any desired period under the Visa Exemption Agreement between the two countries.

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Ordinary Tourist(C-3-9): A person who plans to visit Korea on the purpose of travel for holidays or leisure