I am not aware that a record of Rev. Stephen Bachiler's birth or baptism has been found. Likewise, there seem no known records that call out the names of his parents. The authorities consulted and listed below do not associated the Hampton found with either a father or a mother:
Robert Charles Anderson (1995), ''The Great Migration Begins: Immigrants to New England 1620-1633 ...'', volume 1 article about Stephen Bachiler ...
George Freeman Sanborn, Jr. (1991) , "Rev. Stephen Bachiler of Hampton: Some Additional Information," published in The New Hampshire Genealogical Record. With the authors' consent, this article appears as web content on the Lane Memorial (Hampton, New Hampshire) Library]' site.
Charles H. Batchelder (1936) and Carl W. Brage (1985) Batchelder/Bachilder genealogy through Rev. Stephen Bachiler's son Stephen Bachilder : (A correction of the work on this family by Pierce), Carl W. Brage, ed., [manuscript] (1985). This manuscript has been published as downloadable content (in five parts) to the ''Lane Memorial (Hampton, New Hampshire) Library'' site, see "Genealogy of the Batchelder Family of Hampton, New Hampshire."
More than five hundred FamilySearch "User Submitted Genealogies" (Ancestral File, Pedigree Resource File, International Genealogical Index [IGI, submitted entries]) associate a father, Philip, with Rev. Stephen Bachiler. Philip's wife's name is seen frequently as "Ann Flanders."
Lane Memorial (Hampton, New Hamsphire) Library hosts various content about Rev. Stephen Bachiler. Of the attempts to associated the Hampton founder with a father Philip, the library has posted this notice (emphasis added).
All references that may be found in various places on the Internet to his "father" Philip Bachiler are incorrect and should be ignored or, preferably, corrected.
The notice continues, "Much research has been done to search for his parentage in England, but to date there has been no success."
For the most part, parent-child relationships reported on WikiTree between Philip Bachiler and Rev. Stephen (PGM//PPP) have been severed.
The relationship remains reported on one pair of WikiTree profiles. See "Philip Batchiler" and Rev. Stephen Bachiler. Collaboration has begun to support severing that relationship so that the resultant profile can be merged appropriately.
 Robert Charles Anderson, The Great Migration Begins: Immigrants to New England 1620-1633, Volumes I-III', 3 vols. (1995), 1:61-69, Stephen Bachiler; digital images AmericanAncestors.org (accessed 2013).