Let us tackle this lengthily, for you to grasp the whole concept of your case. Under Philippine laws, a person who has already been previously married may only be allowed to validly contract another marriage upon its dissolution, or upon the declaration of the presumptive death of the first spouse. This rule, however, does not apply to Muslim men who are allowed, under Muslim laws, to have over one wife but not more than four at a time provided he can deal with them with equal companionship and just treatment as enjoined by Islamic laws (Article 27, Presidential Decree No. 1083). Non-Muslims who contract another marriage during the subsistence of the first marriage may be held liable for the crime of bigamy defined and punished under Article 349 of the Revised Penal Code, to wit:
“Article 349. Bigamy.—The penalty of prision mayor shall be imposed upon any person who shall contract a second or subsequent marriage before the former marriage has been legally dissolved, or before the absent spouse has been declared presumptively dead by means of a judgment rendered in the proper proceedings.”
The second spouse may also be considered as the offended party in the crime of bigamy, especially when the latter married the accused without being aware of his previous marriage (People of the Philippines vs. Ricardo Nepomuceno, Jr. y Bernardino, G.R. No. L-40624, June 27, 1975).
Hence, since you just recently learned of your boyfriend’s prior marriage, your BF maybe filed a criminal case for bigamy against him before the prosecutor’s office of the place where you contracted your marriage (This requires the 2nd Wife's Participation).
To successfully prosecute your BF, the second wife must prove the following elements: 1) Her husband is already legally married; 2) his first marriage has not been legally dissolved or, in case his spouse is absent, the absent spouse could not yet be presumed dead according to the Civil Code; 3) he contracts a second marriage; 4) the second or subsequent marriage has all the essential requisites for validity (Luis B. Reyes, The Revised Penal Code, Book II (15th Edition), page 917).
As to your last question, it is the second wife that may have their marriage nullified for being bigamous (Article 35, Family Code of the Philippines). She may do so by filing a petition for the declaration of nullity of their marriage before the Family Court of the province or city where she or your BF has been residing during the course of their bigamous marriage, or in the case of a non-resident respondent, where he may be found in the Philippines, at your election (Section 4, Rule on Declaration of Absolute Nullity of Void Marriages and Annulment of Voidable Marriages, A.M. No. 02-11-10-SC, March 04, 2003).