For starters, as the description states the game difficulty has to be set to medium in order to pop this trophy. This cannot be changed mid bout so you will just have to tough things out yourself, however I've found that a 30 second time limit helps wonders.
The rival teams pop up prior to facing the oni team, and usually pose a decent challenge. I'm not 100% certain if it can be the same teams, however it helps your title progress if you go through arcade with different characters as each character has one for completion and another for completion of hardest.
Anyway, I've noticed you only get rival battles with teams that belong together for example Juri and Bison, Ryu and Ken etc. If you are curious as to who is partnered with who keep an eye on the pairings in arcade as I've noticed they are fitting. You can tell who is compatible if you look at the character select screen the characters are in pairings. I'll post the teams either way...
Guile/Abel
Heihachi/Kuma
Chun Li/Cammy
Ryu/Ken
Kazuya/Nina
Zangief/Rufus
Dhalsim/Sagat
Jin/Xiaoyu
Yoshimitsu/Raven
Balrog/Vega
Bison/Juri
Asuka/Lili
Howarang/Steve
Rolento/Ibuki
Paul/Law
Julia/Bob
Poison/Hugo
King/Marduk
Akuma and Ogre however do not have partners.
FailedSeppukku over on TA also confirmed you can lose at the Pandora fight and the rival fight will still count. You can complete the game for the bonus title or two if you are on hard, however titles are nothing to stress about given the number you get between both the trials and online matches matches.
Thanks Urashima Izumi and Duwen over on TA we have a bit more to offer as far as this achievement goes. Here is a list Duwen provided as far as which fighters will bring about which rivalry...
Guile & Abel -> Heihachi & Kuma
Chun-Li & Cammy -> Lili & Asuka
Ryu & Ken -> Kazuya & Nina
Zangief & Rufus -> Bob & Julia
Sagat & Dhalsim -> Paul & Law
Balrog & Vega -> Yoshimitsu & Raven
Juri & Bison -> Heihachi & Kuma
Rolento & Ibuki -> Marduk & King
Poison & Hugo -> Hwoarang & Steve