How can I apply for Mexican visa

If you are a permanent resident of Japan, no visa is required to enter Mexico at all:

No requerirá visa mexicana el extranjero que presente alguno de los siguientes documentos:

a) Documento que acredite residencia permanente en Canadá, Estados Unidos de América, Japón, el Reino Unido de la Gran Bretaña e Irlanda del Norte, o cualquiera de los países que integran el Espacio Schengen. source

Translated:

A Mexican visa is not required for a foreigner who presents one of the following documents:

a) A document of accredited permanent residency in Canada, the United States of America, Japan, or the United Kingdom of Great Briton and Northern Ireland, or any of the countries in the Schengen Region.

All you need to do is show up in Mexico, present your passport and your Japanese residency card/papers and they will give you a permit upon arrival in Mexico, typically good for 180 days.

For completeness sake, if you don't have residency status in Japan, then you can see the list of requirements for a tourist visa to Mexico for Filipino citizens on the web site for the Mexican Embassy in the Philippines. Be sure to read the specific requirements, but basically:

• Fill out the VISA application form
• Bring appropriate IDs
• Prove that you have economic solvency

These requirements appear to be identical to the ones explained on the Mexican Embassy of Japan site, as well, but on the Filipino site they are in English, on the Japanese site, in Spanish.

As you are not in the Philippines, you will need to do the application process at your nearest embassy or consulate--consult the list of Mexican consulates in Japan.

You will need to fill out the visa application form, available in Spanish and Japanese from the web site for the Mexican Embassy in Japan. It's unclear whether you must fill out this exact form, or if you could fill out the English form, if you're more comfortable with English. I used the English form, which appeared to be the same (from memory) as this one.