This guide is for WiiU/Wii. First, make sure difficulty is on Easy. (Options > Difficulty > Easy)
Then head to Story Mode. Pick New Game and choose Destoroyah. (This run consists mostly of abusing Destoroyah's Fierce Attack.)
Also to note, WiiU saves about 2-3s between each load over Wii. (To my knowledge.)
NEW ROUTE: Removed Osaka - Basic Training for Tokyo - Scratching an Itch, saving ~30s and removed Monster Island - Ganging Up for London - Ganging Up, saving ~10s. (LUCK DEPENDENT)
Time starts on selection of first level. (Route includes obtaining all 7 Power Surges throughout the run.)
Day 1 - Seattle 1 - Rampage: Pick Seattle and turn 90 degrees to the right, walk down the road until you reach the top of the intersection, wait until In-game Timer hits 9:40 then use Fierce Attack + swing down to hit Anguirus while in spawning animation, use Fierce Attack + swing down to kill Anguirus.
Day 2 - San Francisco 1 - Taste Of Power: Pick San Francisco and head into the city, use Fierce Attack + swing down to kill Mechagodzilla 2. (Radiation Surge is obtained.)
Day 3 - Seattle 2 - Trouble Brewing: Pick Seattle and head right, pick up a building and throw the building at Megaguirus then use Surge Attack, Fierce Attack + swing down to kill Megaguirus. (Fire Surge is obtained.)
Day 4 - Osaka 1 - Easy Prey: Pick Osaka and head straight, use Surge Attacks, Fierce Attack + swing down to kill Mechagodzilla 2.
Day 5 - Tokyo 1 - Splashdown: Pick Tokyo and head straight, use Surge Attacks, Fierce Attack + swing down to kill Mechagodzilla.
Day 6 - Monster Island 1 - Poison Alliance: Pick Monster Island and head straight, use Surge Attacks, Fierce Attack + swing down to kill Krystalak and Anguirus. (Killing King Ghidorah and Anguirus or only Anguirus works sometimes for some reason.)
Day 7 - London - Gyozen's Grudge: Pick London and head straight, use Punch + swing left/right and Kick + swing left/right Attacks to kill Jet Jaguar. (Preferably neutral Punches.) (Jet Jaguar is immune to Radiation Surge, Fire Surge, and Destoroyah's Fierce Attack in this level.) (Darkness Surge is obtained.)
Day 8 - San Francisco 2 - Shakeup: Pick San Francisco and head into the city, use Surge Attacks, Fierce Attack + swing down to kill Fire Rodan.
Day 9 - Tokyo 2 - Scratching an Itch: Pick Tokyo and head straight, use Surge Attacks, Fierce Attack + swing down to kill Obsidius.
Day 10 - Osaka 2 - Gassed: Pick Osaka and head straight, use Surge Attacks, Fierce Attack + swing down to kill Obsidius. (Electric Surge is obtained.)
Day 11 - Seattle 3 - Big Trouble: Pick Seattle and head into the city, use Surge Attacks, Fierce Attack + swing down to kill Critical Mass King Ghidorah.
Day 12 - Monster Island 2 - Power Overwhelming: Pick Monster Island and head straight, use Surge Attacks, Fierce Attack + swing down to kill Fire Rodan. (Speed Surge is obtained.)
Day 13 - New York - Gyozen's Plan: Pick New York and head straight, pick up a building and head left, throw the building at Fire Rodan then use Fierce Attack + swing down to kill Fire Rodan, head back to spawn point and wait for the Atoragon, use Surge Attacks, Fierce Attack + swing down to kill the Atoragon. (Doing this level on Day 13 consistently spawns the Atoragon early upon only killing Fire Rodan to my knowledge.)
Day 14 - Tokyo 3 - Rumble in the Surf: Pick Tokyo and head straight, use Surge Attacks, Fierce Attack + swing down to kill Megaguirus. (Shield Surge is obtained.)
Day 15 - Sydney - Desperate Stand: Pick Sydney and head straight, use Surge Attacks, Fierce Attack + swing down to kill King Ghidorah. (Crystal Surge is obtained.)
Day 16 - San Francisco 3 - Defense Alliance: Pick San Francisco and head left, use Surge Attacks, Fierce Attack + swing down to kill Mechagodzilla 2, Jet Jaguar, and Mothra. Mothra Early: Mothra Early is a glitch that is possible in all levels that include Mothra, where Mothra instantly spawns out from her larval state underneath the level within the first second of the in-game timer countdown, this saves a significant amount of time from the original way how this level is suppose to work, ~30s or more, use Surge Attacks, Fierce Attack + swing Down to kill Mechagodzilla 2, Jet Jaguar, and Mothra. (You want to kill Mothra first when this occurs, killing either Mechagodzilla 2 or Jet Jaguar before Mothra after the glitch happens, she will spawn back at her normal spawn.) I have theorized a potential setup for this glitch to work semi-consistently, by manipulating the monster intro cutscenes and holding forward around the second the In-game Timer reaches 9:58, as shown here. This is without Mechagodzilla 2 aggroing, which seems to be luck dependent. I still believe the Mothra Glitch is just random pure luck for now.
Day 17 - Monster Island 3 - Ganging Up: Pick Monster Island and head straight, use Surge Attacks, Fierce Attack + swing down to kill Anguirus and Fire Rodan. (London - Ganging Up is ~10s faster having to only killing King Ghidorah, but may have luck involved, as it worked previously, but when starting a new game, it does not complete when only killing King Ghidorah.)
Day 18 - Osaka 3 - Flight Of The Atoragon: Pick Osaka and turn around and head to the intersection, stay neutral and wait for the Atoragon, use Surge Attacks, Fierce Attack + swing down to kill the Atoragon.
Day 19 - San Francisco 4 - Tyrant: Pick San Francisco and head straight, use Surge Attacks, Fierce Attack + swing down to kill Mechagodzilla, Jet Jaguar, Anguirus, Gigan, Moguera, and Fire Rodan. (Leave Surge Attacks for Moguera and Fire Rodan.)
Time ends on the final hit of the last monster in the final level.