It is possible to do all the trophies in one playthrough, but you have to reach the point where each faction asks you to enlist the boomers. That is the point where you have to choose a faction definetly. It may take a while but that's the only way for sure.
That actually depends on who you do it for first.
If you start the Yes Man line first you can get to the point where you are working on
Wild Card: Side Bets and have dealt with the non-Strip factions* before having to make a choice. At that point you can make a 'hard' save and use it as a starting point for the Legion or NCR line, as you see fit. Completion of
Side Bets will lock you into the Yes Man line regardless of whether or not you have installed him in the Lucky 38's mainframe (technically you have to do that first, but YM's dialogue options allow you to get
Side Bets regardless), so plan accordingly.
In order to do the House line as well, you can start
Wild Card: Change in Management and save at the point where you are asked to replace House with Yes Man (which will be almost immediately after getting the chip from Benny); this will give you the option to not do the switch and work with House.
*Dealing with the Strip factions sets off triggers in certain NCR and Legion sub-quests that will make them hate you, while dealing with the non-strip ones does not, for whatever reason.