Felix will be on a narrow elevator which goes up along a skyscraper, and enemies will jump down and try to fight Felix off the platform. Different strategies work best for different number of opponents.
Four opponents:They often come in "waves" of four opponents. Your most valuable move is the hurricane kick which can throw three of them off the platform. (Press S + D simultaneously.)
Watch the green meter, it'll be reduced by the hurricane kick. Try to time it so the green meter recovers a little before each new wave of opponents, and do the hurricane kick (once for wach "wave") to effectively reduce the amount of opponents.
Two opponents:The two opponents that're left may be easily kicked off the platform. I prefer the kicks over the punches as they seem to reach farther, bumping the opponents away.
One opponent:When there's only one opponent left, it's best to just throw it off the platform. (Press A button to grab him, then A to throw him)
Various hints:If an enemy jumps, quickly kick them before they land to make them fall over and lie on the ground, that will give you time to defeat them one by one.
Haha, that reminds me of when Otacon tries explaining "one for all, all for one" with "they'll gang up on you" 
Watch out for the following!Sometimes a new platform appear, always jump over to the new platform, because the previous one will probably plunge to the depth-death below.
Never give the opponent time to grab you, because they're likely to throw you off the platform and you must start from the beginning.
Two opponents close to each other are nearly impossible to throw because the one you don't grab may break the grab with a punch.
- With those strategies it's possible to clear the first elevator level.
Rooftop Hop:On the second level Felix fights groups of enemies on rooftops, it's generally easier since the rooftops are larger than the previous elevator.
The only new advice is, if you can't see the next rooftop, jump carefully to the left, but not too far because that might take you
over that next rooftop, and you fall down. I don't want to spoil the rest
Feel free to add anything, there are probably some even better strategies, too.