Forza Horizon contains a total of 70 Achievements that are worth 1,500G spread across the base game, one free DLC (the 1,000 Club Expansion Pack), and one Paid DLC (the Rally Expansion Pack).
Even if you opt not to purchase the Rally Expansion, downloading and playing the 1,000 Club Expansion really is a no-brainer and worth doing as it adds to the fun of the game and encourages you to expand your garage, which will help in acquiring points in the Forza Rewards Program -- which you should also be participating in!
The following are Achievements from the Base Game and require no further investment of funds or downloads to obtain, just in-game activities:
...and across the line! (10G)
You competed in your first race at Horizon.
All Your Race Are Belong to Us (30G)
You've won every single race in the game!
Almost Famous (20G)
You're the 50th most popular driver at Horizon.
A Wristed Development (20G)
You received your Yellow Wristband.
Bargain Shopper (10G)
You bagged yourself a nice discount.
Barn This Way (5G)
You found your first barn find.
Been There, Done That! (10G)
You've fully explored the Horizon Festival Loop.
Black Friday (20G)
Never pay for an upgrade again!
Born Slippy (10G)
You've won your first Mixed-Surface or Dirt Race.
Close Encounters (20G)
You've challenged and beaten 10 festival racers on the spot.
Cruise Club (20G)
You've completed 10 free roam challenges online.
Darius Who? (100G)
You owned Darius Flynt and became the Horizon Festival champion.
Ding! (5G)
You got to Level 5 online.
Domination! (10G)
You've sent every Horizon Star packin'.
Exhibitionist (20G)
You've won every Showcase Event in the game.
First! (20G)
You won your first race at Horizon.
Freshly Squeezed (40G)
You received your Orange Wristband.
Gettin' It Done (30G)
You rocked every single Festival Event.
Going Green (25G)
You received your Green Wristband.
Golden Boy (50G)
You received the Golden Wristband.
Hard Driving (10G)
You finished in first place on HARD? Nice.
Just Me and the XP (10G)
You've reached level 25 online. Did you win a car yet?
Killer Skills (25G)
You're the 10th most popular driver at Horizon.
Kudos to You (10G)
You've completed 5 Sponsorship challenges.
Lawbreaker (10G)
You blasted past 5 speed traps and 5 speed zones.
May The Forza Be With You (10G)
You received Free Cars for being a loyal Forza fan!
Noob No More (20G)
25 online races complete… awesome!
Notorious (30G)
You're the most popular driver at Horizon.
OMG (5G)
You won your first car online.
OMGWT*BBQ!? (20G)
You got seriously lucky and won 5 cars online.
One to Watch (10G)
You're the 200th most popular driver at Horizon.
Out of the Blue (30G)
You received your Blue Wristband.
Playground Games (5G)
You completed each of the Playground game types. How fun was that?
Purple Reign (45G)
You received your Purple Wristband.
Racing for Pinks (35G)
You received your Pink Wristband.
Rave Paint (10G)
You created a paintjob and your ride is looking SWEET!
Road Trip (25G)
You've driven along every road in the entire game.
Sellout (20G)
20 Sponsorship Challenges? Now you're popular and rich!
Still a Noob... (10G)
10 online races complete… not bad!
Stuntman (25G)
You've completed every Horizon Outpost PR Stunt.
Swings and Roundabouts (20G)
You've completed 3 of each Playground game types.
Take Her for a Spin! (15G)
You bought a car from the Autoshow. Now take her for a spin!
The Next Big Thing (15G)
You're the 100th most popular driver at Horizon.
Vendetta (20G)
You've beaten a Rival time in 10 events.
WARNING!!! DANGER TO MANIFOLD (15G)
You've won 10 Street Races.
Welcome to Horizon (10G)
You arrived at Horizon Festival raring to go.
Wheelin' 'n Dealin' (10G)
You sold something via your Storefront. KERCHING!
Win Diesel (30G)
You cruised past the competition and won every Street Race.
ZOMG! (10G)
You've won 3 cars online.
#WINNING! (15G)
You've dominated 10 Festival Races.
This first Expansion Pack to the Base Game is Free, and includes a total of 10 new Achievements worth 250G -- the bulk of which are unlocked by obtaining racing medals in the game using specific cars or car makes.
The following Achievements make up the 1,000 Club set:
Ferrari Fan (20G)
Earn a Medal in 14 different Ferraris.
Ford Champion (20G)
Earn a Medal in 13 different Fords.
Forza Legend (80G)
Earn a Medal in 146 different cars!
It's Just Money (20G)
Earn a Medal in 14 different cars worth at least 1 million Cr.
My First Challenge (10G)
Earn your first Medal.
Nissan Ninja (20G)
Earn a Medal in 7 different Nissans.
Sir Challenge-a-Lot (20G)
Earn a Medal in 20 different British cars.
Snake Charmer (20G)
Earn a Medal in 3 different Shelbys.
Well Engineered (20G)
Earn a Medal in 10 different BMWs.
The second major content expansion for the base game is the first paid Expansion Pack, which costs $19.99 USD and contains a total of 10 new Achievements that are worth 250G. This expansion integrates the classic road-rally experience into the game, which seems to be a natural fit considering the environment within which the game is played.
The following make up the Achievements for this Expansion Pack:
Covered in Mud and Glory (20G)
Win a Horizon Rally.
Flawless Victory (15G)
Win a Horizon Rally stage without crashing or using rewind.
Ghostbuster (25G)
Win 10 Horizon Rally stages in online multiplayer.
Harder Driving (25G)
Win a Rally stage on Hard opponent difficulty without using automatic shifting or the Driving Line.
High Five! (20G)
Purchase all five Horizon Rally cars.
Horizon Rally Champion (75G)
Become the Horizon Rally Champion.
Lamborghini Lover (20G)
Earn a Medal in 8 different Lamborghinis.
Mile High Club (10G)
Get a total of 1609 metres of air in Horizon Rally events.
Now that's a Special Stage (20G)
Complete your first Horizon Rally stage.
Rally Rivals (20G)
Complete 5 Horizon Rally events in Rivals mode.
Take her for a Power Slide (20G)
Obtain your first Horizon Rally car.
It should be noted that the new Forza Rewards Program includes points both for unlocking the Achievements in the game -- including those that are part of the expansion packs -- and for obtaining the expansion packs themselves. If you are participating in the Forza Rewards Program (and you should be) obtaining as many of the Achievements above is a very good idea.