Overtime Mode.Pick Overtime mode and try to avoid the special agents where possible.
To unlock Overtime you must complete all the story Case Files in 72hr Mode and be at the heliport at Noon on the final day, after the cutscene you'll go into Overtime mode.
(Once you've done Overtime it'll be selectable from the Main Menu so don't worry if you miss this achievement on your first playthrough.)The aim of Overtime is to collect all the items and bring them back to Isabelle.
For the achievement, You must do this without being knocked out- Being captured by the soldiers. If you're caught at any point and are tied up in the helicopter then you'll have to reload your save.
(Or restart if you haven't been saving.)Dealing with Special AgentsThe easiest method of dealing with the Special Agents is to use the Real MegaMan Buster, Not only does it have enough ammo to see you through Overtime it's also the most powerful weapon in the game.
To unlock it you have to go into 72hr mode then kill 53,594 zombies in that playthrough
(Zombie Genocider achievement) you'll then unlock the Real MegaMan Buster.
Important: Be sure to finish the mode and save otherwise you won't unlock the RMB.
When you have unlocked the RMB it'll be sitting in the Security Room for you.
(It is located in the corner by all the shopping bags with your unlocked outfits. -Behind the ventilation shaft.)Notes:Stay away from the clock tower in the Leisure Park until you've finished collecting everything, Doing so make traveling between malls easier as you'll be able to go out into Leisure Park without the helicopter showing up.
If you're caught you can reload your save, So be sure to save often to avoid any screw ups.
Skateboards are very useful for getting around quickly. Grab a few skateboards from a sports shop.
Entrance Plaza
1F -Jason Wayne's Sporting Goods
2F -Shooting Star Sporting Goods
Paradise Plaza
2F -SporTrance
Wonderland Plaza
2F -Kokonutz Sports TownThere are also three Skating books you should take too to get the most out of a skateboard:
Wonderland Plaza
2F -Sir Book-a-Lot (Skateboarding Magazine)
Paradise Plaza
1F -Contemporary Reading (Sports Magazine)
2F -Bachman's Bookporium (Entertainment Magazine)
The books in Paradise Plaza extend the use of the skateboards and the magazine in Wonderland Plaza gives the ability to ollie on the skateboard, which is useful for jumping over small obstacles such as low fences, railings, ledges, etc.
If there is anything else of use to add or mistakes to fix leave a comment with the information.
Hope this helps, Good luck.