This is a guide to completing Resident Evil: Revelations 2 on Countdown Mode. In this mode you have a set amount of time and can only add time by killing enemies and picking up time bonuses. I would suggest trying to run past as many enemies as possible as it often takes longer to kill them than the time you get for doing so.
The hardest part in my opinion is the beginning of Barry's episode because there will not be very many time bonuses in the prison area because you have already cleared it with Claire. You'll need to run straight to the objectives and get out of there as quickly as possible. If you can avoid using the fire bust on Claire's episode, it would make this level much easier, but it can be done even if you use the bust. Below is my successful run, so you might get some idea of good spots to engage vs run past enemies and a workable path through the level. This is a Live playthrough, so hopefully it is entertaining as well as helpful.
EDIT: Dabigamc pointed out a nice tip for the fire bust room: Once you get to the fire bust room. As soon as you use the cog run to the far left corner and crouch under the spinning blades. They wont kill you and all the enemies will just run into the blades and rack up a good 2-3 minutes, then have moira pry the bars and deal with the few enemies that continue to respawn. I had 4 minutes 20 secs lifting the shutter to go outside.