These are all the achievements which unlock trophies on the in-game Achievements page. Keep in mind, as the game says:



Day Tripper
"Get to the finish line in grand tour mode."

All routes acceptable. No winning necessary.


Five Nights
"Get to all the exits in grand tour mode."

Finish Grand Tour with each of the five possible final stages:

• Akagiyama
  
• Highgate Cemetery
  
• Metropolis
  
• Neon City
  
• Parthenon

Akagiyama can only be accessed by taking the left route all four times. Parthenon can only be accessed by taking the right route all four times. No winning necessary. Each exit fills in an "Exits Found" notch on the save file select screen.


Highway Star
"Defeat all the rivals in a single grand tour run."

All paths acceptable.


Grand Touring
"Complete each track in grand tour mode at least once."

Choose Grand Tour routes with each of the following 15 tracks:

• Morning City
  
• Marble Garden
  
• Resort Islands
  
• Ice Cap
  
• Villa Rica
  
• Chemical Plant
  
• Valley of the Kings
  
• Emerald Hills
  
• Monument Valley
  
• Oil Ocean
  
• Akagiyama
  
• Highgate Cemetery
  
• Metropolis
  
• Neon City
  
• Parthenon

No winning necessary. Each track fills in a "Tracks Visited" notch on the save file select screen.


No Road Not Taken
"Complete all possible routes in grand tour mode."

Finish Grand Tour following each of the 16 possible routes, where L is Left and R is Right:

• LLLL
  
• LLLR
  
• LLRL
  
• LLRR
  
• LRLL
  
• LRLR
  
• LRRL
  
• LRRR
  
• RLLL
  
• RLLR
  
• RLRL
  
• RLRR
  
• RRLL
  
• RRLR
  
• RRRL
  
• RRRR

No winning necessary, but it is best to go for this and Perfectionist I simultaneously. Each route fills in a "Routes Taken" notch on the save file select screen.


Perfectionist I
"Reach every exit defeating all the rivals along the way."

Same as No Road Not Taken, but with maximum winning necessary. Best to go for this and No Road Not Taken simultaneously.


Ruby Cup
"Win Ruby Cup."

Place first at the end of all five Grand Prix Ruby Cup races. Does not require placing first in each individual race. Fills in a "Cups Won" notch on the save file select screen.


Sapphire Cup
"Win Sapphire Cup."

Place first at the end of all five Grand Prix Sapphire Cup races. Does not require placing first in each individual race. Fills in a "Cups Won" notch on the save file select screen.


Emerald Cup
"Win Emerald Cup."

Place first at the end of all five Grand Prix Emerald Cup races. Does not require placing first in each individual race. Fills in a "Cups Won" notch on the save file select screen.


Diamond Cup
"Win Diamond Cup."

Place first at the end of all five Grand Prix Diamond Cup races. Does not require placing first in each individual race. This Cup is only available after winning the other three Cups. Fills in a "Cups Won" notch on the save file select screen.


Invincible
"Win all the races in a single cup."

Place first in each individual race of any single Grand Prix Cup. You can restart a race from the pause menu without penalty, but if you finish a race without placing first and let the game save you'll have to reset the entire Cup.


Perfectionist II
"Win all the races in every cup."

Place first in each individual race of the following 4 Grand Prix Cups:

• Ruby
  
• Sapphire
  
• Emerald
  
• Diamond

You can restart a race from the pause menu without penalty, but if you finish a race without placing first and let the game save you'll have to reset the entire Cup.

Unrivaled
"Defeat every rival character in arcade mode at least once."

"Arcade mode" is just another phrase for Grand Tour in this game. Since rivals are chosen randomly, you can just keep running Grand Tour mode until you get lucky and encounter your missing rivals. Defeating rivals in Cannonball mode DOES NOT COUNT. Each rival defeated in this manner fills in a "Rivals Defeated" notch on the save file select screen.


Versatile
"Win a race with each car model in quick race mode."

Place first in Single Race mode once with each of the five car choices:

• Type23
  
• Epsilon
  
• Arashi
  
• Lynx
  
• Aurora

Each win with a new car fills in a "Cars Used" notch on the save file select screen.


Supersonic
"Stay on the slipstream for more than 15 seconds in any mode."

To stay on a Slipstream you can ram into the back of a car to push it forward and slow yourself down slightly, or move into position behind another car before the Slipstream expires. To ensure there are always cars nearby, play in Cannonball mode with High Traffic Density, 15 Racers, and Rivals On. Might take some time depending on skill and RNG.


Minimalist
"Win a race in grand prix mode without any car upgrades."

All cups acceptable, but Ruby is probably the easiest option for most players. Avoid buying any upgrades before the first race of any cup, then place first in that race. You can restart from the pause menu without penalty.


Intangible
"Complete a grand tour stage without touching anything."

Avoid touching barricades or obstacles of any sort, including other cars, for one full stage of Grand Tour mode. All stages acceptable. No winning necessary. There's no special trick here: success will depend on skill, memory of the track, and traffic RNG.


Perfectionist III
"Complete everything."

"Everything" refers only to the other achievements which unlock trophies on the in-game Achievements screen.


Trophy Dash
"Win a cannonball race of 5 or more tracks."

All tracks acceptable. All options can be adjusted, but you need at least one other racer and at least five tracks. You must place first at the end of the final track. Rivals do not matter with regards to this achievement.


Unchallenged
"Defeat all the rivals in a cannonball race of 5 or more tracks."

All tracks acceptable. Traffic Density, Racers, and Tracks options can be adjusted, but you need at least 5 tracks. Obviously, Rivals must be enabled. You must defeat each rival you encounter. Racers do not matter with regards to this achievement.


Endurance Rally
"Win a cannonball race of 15 tracks or more."

All tracks acceptable. All options can be adjusted, but you need at least one other racer and at least 15 tracks. You must place first at the end of the final track. Rivals do not matter with regards to this achievement.


All Night Long
"Win a cannonball race of all 5 nighttime tracks, in any order."

Set up a Cannonball race with exactly five tracks, then select the following tracks in any order:

• Akagiyama
  
• Highgate Cemetery
  
• Metropolis
  
• Neon City
  
• Parthenon

Traffic Density, Racers, and Rivals options can all be adjusted, but you need at least one other racer. You must place first at the end of the final track. Rivals do not matter with regards to this achievement.


Full of Secrets
"Win a cannonball race of all 5 secret tracks, in any order."

Set up a Cannonball race with exactly five tracks, then select the following tracks in any order:

• Aquatic Ruins
  
• Virtual Plaza
  
• Mystic Cave
  
• Polygon Peaks
  
• Stardust Speedway

Traffic Density, Racers, and Rivals options can all be adjusted, but you need at least one other racer. You must place first at the end of the final track. Rivals do not matter with regards to this achievement. These five tracks are only available after completing Diamond Cup in Gran Prix mode.


Chicken Dinner
"Win a battle royale match."

Place first at the end of Battle Royale mode. Avoid being in last place at the end of any track.

These are all the achievements which do not unlock trophies on the in-game Achievements page. Keep in mind, as the game says:



Deja Vu
"Defeat Tofu Boy in Akagiyama."

Translucent Black Capes
"Defeat Camilla in Highgate Cemetery."

Nothing Personal
"Defeat Alex in Metropolis."

Wall Street Racing
"Defeat David in Neon City."

The Joy of Racing
"Defeat Norman in Parthenon."


These five achievements are not required for Perfectionist III. Each of these achievement requires defeating a specific rival in a specific track. Grand Tour and Cannonball modes are both acceptable. You can hope to get these at random while playing normally or going for the other achievements, but you will probably have to seek some of them out. There are two great methods for hunting these guys:

Option 1 is arguably the fastest, but also requires the most skill. Make sure Rival Messages are On in the game settings. Setup a Cannonball race with these settings: Traffic Density High, Racers 15, Rivals On, Tracks 1. Choose the track needed for the achievement you are trying to complete, as listed below. If you see the rival you need then race as usual; if you see any other rival, reset from the pause menu. Repeat until complete. You will probably need to utilize the Slipstream mechanic frequently and precisely in order to defeat a rival due to the slow start mechanic, which is why I recommend High Traffic Density and 15 Racers. More potential Slipstreams = better chance of winning!

Option 2 is slower, but much easier. Setup a Cannonball race with Rivals On and Tracks 5. Adjust Traffic Density and Racers settings to your liking. Set all tracks to the track needed for the achievement you are trying to complete. Each lap will give you another randomly selected rival, and it will likely be easier to defeat rivals after the first lap due to the slow start mechanic. Keep running the same track until you complete the desired achievement, then repeat for the next.