You'll begin outside the Sedgewick Hotel, and your goal is to escort Ecto-1 close enough to deal with the Stay-Puft Marshmallow Man. The condition of the street won't make it easy. Stay-Puft is producing Marshmallow Minis that harass you like hounds. Attack the Minis to blow them up, but then Hobo Ghosts appear; their ranged attacks can hurt. The good news is that you won't need to deploy traps; Ecto-1's Super Slammer is a rolling instant ghost trap. Sap and cap the ghosts, then wrangle it over Ecto-1 to let it do the trapping. Eventually, a car thrown from Stay-Puft will clear the way down the block. Continue attacking the Marshmallow Minis and trapping the Hobo Ghosts. Eventually, Winston will note the flapping of wings.
Ghosts and Gargoyles
Now you have Stone Gargoyles assaulting you from above. They're hard to break up with your Blast Stream, but they have a weakness. If you'll note their PKE gagues, they're always red. By manually engaging the Capture Stream on them and then slamming them to the street or nearby buildings, you can break them up very quickly. Since they're so dangerous and yet so quick to dispatch, try to go for them first when you see them. A second wave of enemies will then appear featuring more Stone Gargoyles, Marshmallow Minis, Hobo Ghosts, and even Construction Worker Ghosts; these latter aren't tough but can shoot you repeatedly. Once they're clear, you'll need to find a way for Ecto-1 to keep going. Follow Winston into a nearby laundromat.
Don't worry about the haunted washing machines; they'll simply detour you for a bit. Before exiting the back door, note the water fountain and a Cursed Artifact in a side room.
Outside, you'll spot a leaking gasoline truck embedded in a marshmallow mass, and Egon will reveal the Proton Pack's secondary fire, the Boson Dart, making it available for your use. The Boson Dart is essentially a slow but potent proton rocket. Fire one into the spilling gasoline and back away. The whole mess will blow up, clearing the way for Ecto-1. Follow it down the alley, and keep an eye out for two more Cursed Artifacts. One will be near the dead-end that Stay-Puft eventually opens up; another will be in a side alley near the exit of the alley.
Hindenburg: The Musical
Emerging from the alley, you'll arrive in front of the Opera House, and there are patches of Black Slime along the front of it. Keep away from them, especially since they'll eventually turn into Black Slime Portals. Opera Diva Ghosts will then begin an attack. They can use the Portals to quickly move around; also, Hobo Ghosts and Stone Gargoyles will join in. Keep on the move, but be sure to avoid the Portals. Slam away the Gargoyles and trap all the ghosts. The way to Times Square will now be open.
Shadow of the Stay-Puft
Looks like Stay-Puft's got a goal in mind. You need to get his attention. Hit Stay-Puft with your Blast Stream, but watch out for anything he throws. If it's a marshmallow mass, it will likely turn into Marshmallow Minis on impact. Both the marshmallow mass and the Minis that spawn from it are vulnerable to Boson Darts, though if you hit one too close, you'll get blown back. This unlocks an Achievement, however. Also remember that, with enough funds, you can upgrade the Boson Dart to let you fire more of them before overheating. Once you blow away the Minis, hit Stay-Puft a couple times with Boson Darts. He'll then throw a billboard that clears an avenue of escape for you.
Sprint to keep up with Ray as you head to the next clearing. Keep close to him and continue to destroy the Minis and harass Stay-Puft with Boson Darts. A skillful Boson Dart at the flying marshmallows can keep the Minis from forming. After a few more hits, Stay-Puft should throw debris that clears the way to the third clearing. Repeat the defend and harass process here and Stay-Puft should throw one more piece of debris; this clears the way into the Architect building that Stay-Puft was investigating earlier.
Rush inside, but keep the Blast Stream ready. More Marshmallow Minis will bust in from the doors and windows. Once the way is clear, investigate for a Cursed Artifact, then follow Ray to the elevators.
Race to the Roof
Follow Ray down the hall, but at the end, take the lead. Note the water fountain in the hall, then turn left and proceed slowly, with your Paragoggles out. The PKE meter should point you towards a Drafting room down the hall and to your left. Open the door and continue on inside. Ray will warn about sudden movements, so move slowly. Keep moving towards the center of the room. As the meter begins to peak, get ready to switch back to the Blast Stream because Marshmallow Minis will suddenly drop in from the ceiling vents. Either stick with Ray or head towards the wall to make a stand against a mess of Marshmallow Minis. Sticking with Ray will allow the two of you to help each other out while sticking to the walls limits the Minis' angles of attack. Blast away the Minis with Blast Stream and Boson Darts, and don't limit your shooting to the Minis. Totally wreck the drafting room to unlock this stage's special Achievement.
Puffy White Menace
Once the coast is clear, search the far wall for a Cursed Artifact, then join Ray by the exit, but be ready to deal with a few more Minis that burst in. More will be in the corridor ahead. Ignore Stay-Puft and continue down the corridor, stopping along the way to hunt down a final Cursed Artifact, then enter the smashed-up Conference Room ahead. A woman's there, but don't go after her because Stay-Puft will throw a punch into the room. She'll run away, and you'll have to deal with several more Marshmallow Minis. Only when the way is clear should you follow her down the service corridor. The woman will be there; so will Peter.
Try to head down the stairs, but you'll be blocked. Only one way to go now: up. Ignore the falling debris and keep climbing until you reach the access door to the roof.
Ghosts At Work
Scan the roof with your PKE meter. Several Construction Worker Ghosts will burst out of the roof. Sap, cap, and trap all of them, then approach the edge of the roof with your PKE meter out. As the meter peaks, Stay-Puft will suddenly show up. Help the guys blast him off. He'll fall down but won't make it to the street. Instead, his shaking will cause you to pitch over the edge, though Ray will grab you by your belt.