After completing all objectives, and collecting all cash icons, on each of the levels with a character, you'll unlock Projectives mode (this can be selected on the level select screen by scrolling to the side, the same way you select modes like Hawkman)
In Projectives mode, you have 60 seconds per run to try and complete the 5 "pro-jectives." These do not have to be done all in 1 run, so break it up and save yourself tons of frustration.
Each level has the same type of projective goals, these include:
Getting a Sick score
Collecting C-O-M-B-O
Getting a large scoring Combo
Collecting 8 skateboard collectables
Doing a Boneless over the magic bum
The sick score and large scoring combo objectives increase in value for each subsequent level but if you've managed to complete the game to this point, it shouldn't be too difficult for you. Reverts help a lot if you can find a decent halfpipe or bowl to trick in. I like to use a large combo with varied hold tricks to push the score up quickly, and flip tricks to increase the multiplier faster.
Collectables and the magic bum are not hard to find, and can be seen on the map screen from the pause menu. This screen will even show you the "secret" areas on the levels, and a lot of the skateboards and bums tend to be in those areas, again you should know where these are from collecting the hidden DVDs.
A few of the combo lines can be a little tricky, and if you haven't already I would suggest maxing out your characters grind and manual stats. If you haven't blown your money on things like special tricks, you should have plenty of cash from career mode to make this happen. Most of the combo lines will force you to travel a pretty far distance and push your limits so I would suggest trying to alternate between manuals and grinding to maximize the time you have before things get really touchy on those meters. Again, the letters can be seen on the map screen, and are, for the most part, clearly visible in game, so setting up the line shouldn't be TOO difficult, but a few will test your skills.
Good luck!