The Philippines are accessible all year round, although it's also worth noting that here, weather can be unpredictable. In addition, there are at least four different climate zones, and some islands have their microclimate, which makes classification even more difficult.
In the climate zone of Type I, there is a rather dry phase from November to April, during the rest of the year there is more rainfall. Manila, large parts of Palawan, and Mindoro fall into this zone.

The warmer season, simply called "hot season" by the Filipinos

Consequently, the rainy season follows from about mid-June / early July. Depending on the region, the main focus is seen by the locals in June, July, December, and January.
However, the rainy season does not necessarily mean that rain is to be expected constantly. Often there are only occasional showers, which preferably fall in the late afternoon or at night.
Since temperatures can reach quite high values even during the rainy season, occasional showers are often more likely to be regarded as a pleasant cool-down than as a source of discomfort. Typical for the rainy season is that almost always some clouds pass by in the sky.
Conclusion: What is the optimal travel time for the Philippines?

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December, January, February: Palawan, Luzon, Visayas
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March, April, May: all destinations except climate zone II (see above)
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June, July, August: Siargao, Visayas
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September, October, November: Siargao, Palawan, rice terraces from November
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All year round: Bohol, Camotes, Bantayan, Malapascua, and Leyte. The paradox is that it can rain there all year round because the rainfall is distributed quite evenly. Only Davao seems to be almost continuously well accessible.