The feats that are mentor specific are exactly this, if you are not mentored.
You cannot even ENTER these instances without aid.
The Regal Hotel, Star labs (meta only level 15 instance) wearing your survival suit I believe? the Watchtower, destroy the security cameras in Metro university, etc all on villain side cannot be completed.
It is exactly as you state;
They are mentor specific, so you cannot be the 'first' to enter an instance, because in order to actually enter them, you need to get someone to 'let you in'.
The only plausible workaround at the moment, is to form a group of 5, converted into a raid. Have four players enter first, then the fifth enter, which will net the fifth their own instance. The feats are rewarded normally from this.
Really, just open up all the origin only instances at 30 should be easiest fix. Metro University, Regal Hotel, Watchtower, etc.
I have had no other issues with feats since the initial cleanup except these.