Each time you complete a full section of the mission, the timer extends adding upon the remaining time you have left with what Bungie predicts the next section should take at its longest. So the first portion is 5 minutes. Let’s say you complete in 3. Bungie will then add 16 minutes (not the actual amount of time) so you have a total of 18 minutes to complete the next portion of the mission. So on so forth.

Got it. So there's no secret thing you have to shoot? Still, I hate the timer mechanics. Always have, but that doesn't sound too bad.

There are a few crystals you can shoot to also extend the timer from start to finish there are about 7 crystals that I can recall shooting to extend timer by a minute or 2