I've given up on this achievement. Once I got within one building (a bunker in part of the map that I hadn't explored), but I literally had to save/reload 25 times during the last minute just to get it that close. I can't just go back to a previous save because we're talking about mere seconds here. If I go back and waste even 10 seconds sending a force out to the far corner of the map to take that bunker, I won't have enough seconds to take the last base.
I think I need to seriously develop my skills before I attempt it again. I'm just not good enough.
By comparison, the "Speed Bump" achievement was relatively easy for me. I just massed hunter banelings and moved them to the edge of the main base at the 22 minute mark. I noticed that the Odin will actually start walking towards the exit before it actually gets sent at you. So I killed it with 22:25 on the clock when it was standing right at the front door ready to come out - but it was never really in doubt.
You shouldnt really be cutting it that close honestly. Im not sure what units youre using in your army, but I found mass banelines was the easiest option for me (I used swarmlings and splitter banelings). If you use Kerrigan to clear the Terran base north of your own, while youre getting your economy going, you can expand quickly and really start pumping out banelings, which also serve to defend your bile launchers really well (you need to be vigiliant and keep a force of banelings at your northern expansion for defense).
Some key components to this strategy:
Splitter Banelings (100% increased damage against primary target)
Kerrigan: Kinetic Blast, Crushing Force, Improved Overlords, Spawn Banelings, Twin Drones, Ability Cooldown reduction, Apocalypse
With this strategy I was able to clear all Terran structures (including Augustgrad gates) before the last Bile Launcher even hit the ground.
You need to remember youll need a flying unit to get the Missle Launchers up on platforms near the Wester Augustgrad Gate and near southernmost mini-base.
You also dont technically need to be perfect about defending Bile Launchers, just remember that you can only lose 2, when you lose a third you fail.