How can I "Rub your head on the roof for __ m (in one game)"?

Solution 1:

In order to complete this mission objective, you need to hold your jetpack on so that Barry will stay on the ceiling for the duration of the level. Try to stay on the ceiling at all times, unless there is an obstacle in the way, for the best chance to complete this objective.

Do note however, that staying on the ceiling in a vehicle does not count towards the objective.

Solution 2:

Basically all you have to do is stay with your head against the roof for those 300 meters. It doesn't have to be all in a row, you can come down, but it has to be all in one run.