Need For Speed ProStreet

You can get most of this information in the TA Walkthrough however most people, like me, just check these solution (or do so first), so I thought I'd submit my own. Enough pandering, here's how it goes:

First, if you don't want to create a major speed bump in your progress, go to the menu and select Options > Gameplay > Assist mode and set it to "Casual" then backup to Options > Interface and turn on Best Line (and if you thing it will help Minimap and Turn Indicators. I opted out of those for my runs).

Unfortunately, I did not keep track of the vehicles I started out with before the better vehicles unlocked but here's what I used for a majority of the game. I did not special tune any vehicles other than the Camaro SS for Wheelies that I found on YouTube. Everything else was purchased through Quick Upgrades Level 3 and body upgrades for everything but Speed. I'm not going to give any special pointers as the turning, drifting and braking will pretty happen without any trouble on Casual Assist and you'll pick up some tips of your own on this long grind of a Career Mode. Here's what I used using some research I picked up online:
Grip: Porsche 911 Turbo
Drag: 240SX (S13)
Wheelie: Camaro SS
Drift: RX-7
Speed: Dodge Viper & Zonda

Now...

...you must DOMINATE each Race Day in Career. You don't have to beat or even start every race, unless you need the points, just enough cumulative points to get the "Dominated" message after returning to the Race Day menu area from a race. The Race Day Progress menu item will tell your your progress.
Every spot on the map that offers races must be dominated. You can tell if it's dominated by highlighting a yellow (aka completed) Race Day and waiting for the Area name in the dialogue to flip to your finish result. If it says "DOMINATED", you've dominated it. Otherwise, try again. King and car reward race days also need to be Dominated, but so long as you've won the prize, you've dominated it. Also just be thorough to complete every Race Day so the faded Race Days on the map are visible and you don't miss any of them. As a final note, you'll need to break 10 different track records of each type to open the Kings races.

You may get this after defeating Ryo in the final King challenge, but I assume most people will want to complete all of the King challenges first, then go back for the rest.
Why?
Once all the Kings have been defeated, you won't have to pay for repairs! This didn't help me as much since I learned after I Dominated a majority of the game but I does cut down on costs if you're a risky player starting out. I found the number of markers given for each race day were more than enough to Dominate them.

The achievement will pop after you leave the last Dominated Race Day (when returning to the Career Map).

As stated above, you gotta get enough points to dominate each raceday in career.
Also, you do NOT need to win every race within each raceday. If you can score high, especially in drift and drags, you can eliminate the need to do at least two other races.

Out of all the race types, I reckon that any speed type race in Nevada is the hardest followed by Grip.

With the cars I used I would buy the best parts and then drop the ride height to the ground (Except for Drag and drift)
Here are the cars I used.

GRIP:
- Road runner for the majority of the races. Cheap and powerful
- Porsche 911 NOT the GT2 for the last races.
DRIFT:
- RX8 (average 4500 + per round) Hi Power with crap traction. Excellent combo
DRAG/WHEELIE:
- Pagani Zonda (6.7's quart miles and 1200 wheeliez)
SPEED
- Supra maxed out for most races. Easy to control.
- Ford GT for the last races. Needed to win later speed trap stages. Increase your downforce to the maximum for both cars.

There are a total of 52 events in the career.
It takes 10-15 mins to dominate an event, maybe 20 if you llike me, have trouble with this games driving physics..
In my quick calculation that should be 12-14 hours worth of your life.
But it's real easy, to just win around 75% for Domination of an event, especially if you get good scores.

At the end you'll face off Ryo..
Like some of the other guides said, a good choice is the Porsche Stage 3+ Widebody kit, to get you there. Use it for Grip etc.

I used Supra for Speed, with Stage 2 tuning+Widebody kit.

I had the Charger for Drag, fully tuned.

And focused on winning Aki's RX-7 for Drifting.
Used the Corolla, full engine power+stock wheels slow but easy.

So save your money to buy Drag-power and Porsche 911, is a good advice

Good luck and frustration to you
PS. By the time I wrote this, I was on last Showdown and just Ryo left after.

This is not that hard of an achievement it just takes awhile because of all of the race days. You have to beat every race day and dominate it which usually means about double the points to fully dominate it. Just a tip: Make sure every race day you do dominate it. This means that you shouldn't go and win then leave without dominating it. This will save you time and let you get the achievement faster.