The following actions will gain you the following achievements:
There's a lot of hip hop references here, if you didn't notice. I'm seeing NAS, Wu-Tang, Beastie Boys...
Welcome to Forza Motorsport: Complete your first race.
Buyer's Market: Buy a car in the Auction House.
Wheelin' Dealin': Sell a car in the Auction House.
Bronze Collector: Collect 100 cars.
Silver Collector: Collect 300 cars.
Gold Collector: Collect 500 cars.
Platinum Collector: Collect 700 cars.
Suit Up: Unlock 10 Driver Gear suits.
If The Shoe Fits: Unlock 25 Driver Gear suits.
Decked Ou: Unlock 50 Driver Gear suits.
Fashion Statement: Unlock 100 Driver Gear suits.
Uncommon Collector: Reach Car Collector Tier 2.
Rare Collector: Reach Car Collector Tier 3.
Super Rare Collector: Reach Car Collector Tier 4.
Legendary Collector: Reach Car Collector Tier 5.
Exclusive Collector: Reach Car Collector Tier 6.
Elite Collector: Reach Car Collector Tier 7.
Ultimate Collector: Reach Car Collector Tier 8.
Rennsport Driver: Own the 2018 Porsche 911 GT2 RS.
Paparazzi: Share a Photo.
Show Off: Share a Replay.
Moonlighting: Complete 50 laps at night.
Seeker Champion: Complete the Seeker Championship.
Breakout Champion: Complete the Breakout Championship.
Evolution Champion: Complete the Evolution Championship.
Domination Champion: Complete the Domination Championship.
Masters Champion: Complete the Masters Championship.
Driver’s Cup Champion: Complete the Forza Driver's Cup.
Seeker Elite Champion: Fully Complete the Seeker Championship.
Breakout Elite Champion: Fully Complete the Breakout Championship.
Evolution Elite Champion: Fully Complete the Evolution Championship.
Domination Elite Champion: Fully Complete the Domination Championship.
Masters Elite Champion: Fully Complete the Masters Championship.
Driver’s Cup Elite Champion (50 points): Fully Complete the Forza Driver's Cup Championship.
Show and Tell: Complete all Showcase Events in the Forza Driver's Cup.
Modified: Use your first Mod.
Playing With A Full Deck: Acquire 50 Mods.
Discard Pile: Equip and Fully Use 50 Mods.
Cash Rules Everything Around Me: Earn 500,000 credits from Mods.
I Am Legend: Finish an event and complete all challenges with 3 Legendary Mods.
'Bahn Burner: Complete a race in the 1998 Porsche 911 GT1 Strassenversion on Maple Valley.
Italian Tune Up: Complete a race in the 2014 Ferrari FXX K on Mugello.
Monster: Complete a race in the 2017 Nissan GT-R on Suzuka.
No Substitute: Complete a race with every car from Porsche.
Two-Fifty: Drive faster than 250 mph in any car.
Making It Rain: Create your own weather forecast in Freeplay.
Storm Chaser: Complete a race in every Rain Weather Scenario.
Survival of the Fastest: Complete the Spa-Francorchamps 100 showcase event with Extra Long Race Length enabled.
Paint Booth: Share one of your Paints.
All About the Benjamins: Earn 50,000 credits from the community using your Design.
Tune It Up: Share one of your Tunes.
Skills to Pay the Bills: Earn 50,000 credits from the community using your Tune.
Unrivaled: Beat 10 Rivals while running with no Assists.
Super Human: Win a race with Unbeatable Drivatar Difficulty.
Joy Ride: Enter Test Drive in any car.
Nightvision: Complete 50 laps at night in Multiplayer.
Rain Dancer: Complete 50 laps in the rain in Multiplayer.
Gaining Experience: Complete 100 laps in Multiplayer.
Devoted Racer: Complete 300 laps in Multiplayer.
World Traveler: Complete a race on every track in Multiplayer.
Hard Driver: Win a race with no Assists turned on in a Multiplayer race.
Underdog: Start last and finish first in a Multiplayer race with 24 cars.