Can't Stop Here, This is Brute Country Achievement in Halo: The Master Chief Collection

Before anything, make sure to turn on "Timing HUD" in the Campaign Lobby before starting a mission. This will give you a nice way of tracking your mission time during your playthrough. In order to beat the Par Time on all eight missions with Halo 3: ODST’s Campaign, you will want to take two things into account. 

First, play on the Easy difficulty setting so that enemies aren't as dangerous. Secondly, don't bother turning on any skull modifiers in the lobby. It’s worth noting that unlike the other games in the series, Halo 3: ODST’s missions do not contain many exploits for skipping firefights. What’s more, several of the missions contain “wave defense” or “hold-your-position” segments which cannot be skipped and which will definitely take some time. With these tips in mind, you should have no problem completing each mission under Par Time. 

You can use the checklist below for a reference on each mission’s Par Time:

• Tayari Plaza - 3:00 minutes
• Uplift Reserve – 4:00 minutes
• Kizingo Boulevard – 9:00 minutes
• ONI Alpha Site – 13:00 minutes
• NMPD HQ – 10:00 minutes
• Kikowani Station – 10:00 minutes
• Data Hive – 16:00 minutes
• Coastal Highway – 25:00 minutes

Overall, just remember to play on the lowest difficulty setting and try rushing past as many firefights (when possible). Once you beat the Par Time for all eight missions, this achievement will unlock.