Update, 21st June 2018: Since the June update, all cars can now be upgraded to level 399. This means that you can now buy the level 16 catch up pack as appose to just the Level 11 catch up pack. I've updated the guide to reflect this.
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This solution will be very long winded but, I encourage you to read it carefully and follow the steps outlined. It'll make things so much easier.
Prior to myself tackling the DLC, I had finished the entire base game; all story missions, all activities, all collectibles, all derelicts and all roaming racers. Additionally, I needed to finish the Speedcross DLC missions to unlock the dealership in order to buy the cars. By the end of this (and after spending money and part tokens on cars and parts) I had around $1.8 million in cash and 105 part tokens. A lot of the came from Shipments rewarded from playing the game so, open them when you get them.
Thanks to the February 2018 update adding
Catch-Up Packs, this achievement has become a lot easier to earn. The level 11 pack is available
once you have completed Chapter 3 of the main game and the level 16 pack is available
once you have completed Chapter 5 of the main game. However, there are a couple of things that should be noted:
1. In order to gain access to Speedcross dealership, you
MUST finish all 16 of the missions the game gives you. Do not worry about not having a car, the game provides you with one for the events. These mission are highlighted in a light blue bubble around the map. To make them easier to see, press back button to bring up the map and press

to go to the
Events tab.
2. Both of the Speedcross cars are free to purchase from the dealership
ONCE you have completed the 16 mission the game gives you.
3. You
DO NOT need to have matching part brands (e.g. Outlaw) for all 6 of the components in the tune up shop, they all just need to be level 12 components.
4. It does not matter which car you to choose to upgrade, they both end up at level 299.
Update June 2018: Both cars can go to 399 now5. You are unable to buy the level 16 pack for both Speed Cross cars as neither car can surpass level 299.
Update June 2018: You can now buy level 16 Catch-up Packs6. Both cars are free to purchase from the dealership
AFTER you have completed the story missions for the DLC.
Now that's been outlined, here's how you go about getting the achievement in 10 mins, max.
1. Finish all 16 missions of the Speedcross DLC
2. Head to the dealership located on the west side of the map (light blue shield with the logo of two hands grabbing each other)
3. Purchase one or both cars, preferably both as they both have individual achievements They are both free anyway som you may as well buy both. The cars are:
Mini JCW Countrymanand
Infiniti Q60 S4. Head to a tune up shop, your nearest one is north-west of the dealership (pink shield with the logo of a spanner)
5. Once in the dealership, press

once to get to the
Catch-Up Packs tab
6. Purchase the Level 11 Stock pack for $117,900. This will give you stock level 11 parts on all 6 upgrade areas. You should have made more than enough money from the missions and side bets to purchase this. If not, play a random race a couple times and complete the side bets that are offered to get some extra cash. Important note: I have the deluxe edition which gives you a 10% in game discount on everything. Normal price for non-deluxe edition owners is $131,100Update June 2018, 6. Purchase the
Level 16 Stock pack for
$162,000. This will give you stock level 16 parts on all 6 upgrade areas. You should have made more than enough money from the missions and side bets to purchase this. If not, play a random race a couple times and complete the side bets that are offered to get some extra cash.
Important note: I have the deluxe edition which gives you a 10% in game discount on everything. Normal price for non-deluxe edition owners is $180,0007. Press

once on your controller and head over to the
Buy tab. Here, look for any level 12 parts and buy them. It does not matter what brand they are. Parts will range from $17-$21k depending on their perks and brand.
Now, if you're lucky, you'll be able to buy all 6 parts from here, which will cost you $84-$126k depending on brand and perks. If not, then you'll have to perform a few more step involving part tokens. You get part tokens from trading in old parts you don't want (you'll only get one token back per traded in part) or, from Shipments.
Shipments are given to every time you level up, complete a Speedcross mission or, complete a daily challenges. In these Shipments, you'll be able to find tokens to redeem. I've only seen them handed in variations between 3 and 9.
8. Press

once and head over to the
Equip tab. Check all your parts and make a note of which ones are not level 18
9. Press

again and head over to the
Trade-ins tab. If you have a red exclamation mark next to the tab, you have spins available.
Each spin will cost you 3 tokens.
10. From here, select which part you need to upgrade to level 18 by pressing up or down on the left stick and then press

. It'll lock the part that you want and spin the brand and perk sections only.
11. If you get a level 18 part, select
Equip from the options given below the part. If you get a different level part, select
Trade-in from the options given below the part. You'll get one token back for trading it in but, this token you get back could mean the difference between getting another spin or not.
Once you have equipped level 18 parts on each slot, your achievement will unlock. Enjoy your 50G and DLC completion.