Fred, I doubt anyone will be able to reply from experience but I had a look at the admissions section of the Ateneo site here:
http://law.ateneo.edu/?page_id=72
For me the stand-outs are 1. the entrance exam and 2. the recommendations.
If I were you I'd do the following:
1. email Ateneo's Admissions Dept and ask:
a. For more information regarding the entrance exam. What does it cover and what is the applicant expected to attain.
b. From which school do they prefer applicants to come.
c. What experience have they of admitting applicants from your daughter's (proposed) college in Bohol.
(Of course you may not get direct answers but it's worth having a go).
2. I'd then try and get in touch with someone who has actually studied at, say, Ateneo and ask them similar questions. For example, I'd google "ateneo graduate blog" and you'll find people you can contact. Ask them similar questions to the above.
3. I'd also contact the local Bohol college. I'd ask them for stats regarding students going on to higher education. How many of their graduates went to, say, Ateneo.
If that fails then I have a friend studying for a Masters in Eng Lit at UPD and I can happily ask her.
Finally, academia is snobbish the world over. I know already that my son's Grammar School will open doors in a way that my daughters' Comp won't.
Sorry for such a long post!