Not much to say about this one. Completing Ignition mode within 25 minutes is pretty easy. I would recommend that you play through the game multiple times first (Finishing off every other achievement first) to get familiar with it and choosing a route which suits you best.
You can't do much about the Trace Route hack levels except for using every speed boost and avoiding walls/bostacles, but you can very well decrease your time by creating shortcuts in the Hardware Crack levels. Remember: Your RIG Level carries over to further playthroughs; which means that from now on (if you've reached RIG Level 4, which you'll do after your first playthrough), you are able to use powerups which unlocked at a later point in the game before.
Especially those block-removing powerups are incredibly useful - you will be able to finish levels in a few seconds instead of spending minutes since you can now just go through objects instead of going around them.
System Override hack levels offer your a variety of possible solutions. Using units spawned by pressing Y and A always did the trick for me. What you want to do - since you're under pressure of time - is to try and eliminate all radar-looking enemies with that combo and once you've accomplished that, spam the X button - those units will always choose the quickest way to the exit automatically. Plus: Since you've taken out all radars, no enemy unit will attack you AND they're extremely fast, too. Also: Look for those "instable" blocks, which you can blow up by holding down RT, using those passages will save you a lot of time.
I hope this is helpful. I got the achievement the very first time I've gone for it and I think you will, too!
By the way: Cutscenes don't count towards the time!