Your triple jump is activated by jumping three times. Sometimes the timing can be funny and it might take a bit of practice to get it right. If you can't jump high enough on your own, activate some spinach for a high jumping effect.
Having been a while since I did this quest, spinach may or may not be useable. It is my best suggestion, though.
Easiest way I've found to nail the triple jump is:
Jump 1: SPACEBAR
Jump 2: SPACEBAR
While in midair of Jump 2: SPACEBARSPACEBARSPACEBARSPACEBARSPACEBARSPACEBARSPACEBARSPACEBARSPACEBAR
Levitation, spinach and extra-high jumps don't work in that quest anymore. Plain ol' simple jump is the way to go.
If you are not familiar with platform games, here are a few tips. Time your jumps well and approach ledges with speed to build up momentum. Let yourself walk off that last platform for a fraction of a second, and jump only while falling in the air (yes, you can do that here). If done right, the extra bit of length will be more than enough to clear that gap easily. Good luck! :-)
I tried A Summer's Day a bunch of times a couple of weeks ago and couldn't make that last jump either... then I got an increased walking speed card in my upgrades and tried it again, and made the jump easily! It might be worth it to wait until you get a faster walking speed or higher jumping (if there's an upgrade for that -- I haven't seen one yet), then give it another shot.
Heeeeeyyy! So there was some slight physics changes made to the levels that should now allow all players with different upgrades to make it through the more platform based quests. I won't get into the messy details of it here, but the important thing is that all the bodies are hidden and fingerprints are covered up... Please try the quest again when you can and hope you enjoy it!
I just did Summer's Day on a level 5 Glitch. (Made an alt to play the new content.) I still really dislike the quest because of the timed disappearance of the platforms but it is doable with only the tutorial upgrades. You have to find all the various ways to trigger platforms and jump without hesitation once they appear.