The release notes for Leovold, Emissary of Trest indicates that “If you and a permanent you control each become the target of the same spell or ability an opponent controls, Leovold's ability will trigger twice”. Is it also the case if two permanents you control become the target of the same spell or ability an opponent controls" ?

Yes, you get two triggers. Two permanents were targeted by an opponent's spell or ability, so Leovold will trigger two times. It doesn't matter that the same spell or ability is targeting multiple times, what matters is that multiple permanents of yours were targeted by a spell or ability controlled by an opponent.

Nathan Long
Magic Rules NetRep