Not enough loot boxes on Roosevelt Island for commendation
The island had 8 unlocked boxes and 2 keyed Hyena boxes, but 2 unlocked boxes that were only available after the mission ended. Not enough for the commendation without keys.
Trust me, there are enough loot boxes to get your commendation done. Don´t forget that also those special ammo / grenades / medikits chests count towards it (simply everything with "LOOT" option). Just look carefully in every corner.
Special ammo boxes can be detonated by shooting at them. With 4 people or enough aoe those tend to go off early in a firefight, enemies also can tag them with their own aoes if the fight is near them.