I believe that this achievement requires that the story be completed (feel free to comment if not). It requires you to upgrade the training room to level 10 and complete a level 10 training with any character.
Zeni: Head to a shop and sell any items which say that they are valuable and are just for selling. If you have finished fighting Mira and have cooked 5 full meals, then sell all of your cooking ingredients as well. I also recommend that you wish for Zeni when you use the Dragon Balls. Note that the amount of Zeni changes depending on how far you are in the story. After the story, you get 100,000 Zeni for "I want to be rich!". If you wait till after the story to Summon Shenron 10 times for another achievement, you will end up with 1,000,000 Zeni.
Any Machine Parts: West City --- Fly around the Capsule Corporation on the ground. There are stacks of boxes around the buildings that each have a Machine Part loot spot, as well as next to the Material Shop (Wrench Shop) across the street. After getting all of the loot, enter and then exit Capsule Corporation and repeat. I'm 99% sure you can find any Machine Part here.
Refined Gold: Sacred Land of Korin --- Follow the path southeast from Korin's Tower to a cave. Break the rocks and save / reload until you get 4 Refined Gold.
Black / White Meteorite: Bought from Material Shops (Wrench Shops) in Satan City / Gingertown / Lucca Village after the story.
Total: Zeni x 500,000 --- D Medal x 150
Refined Iron x 2 --- Refined Silver x 3 --- Refined Gold x 4
White Meteorite x 4 --- Black Meteorite x 4
You only need one of each material for each Lvl (except Lvl 10).
Lvl 2: Zeni x 4,500 --- D Medal x 5 --- Sturdy Bolt S --- Refined Iron
Lvl 3: Zeni x 15,500 --- D Medal x 10 --- Gear Bearing S --- Steel Nut S --- Refined Iron
lvl 4: Zeni x 25,000 --- D Medal x 10 --- Sturdy Bolt L --- Sturdy Bolt Z --- Refined Silver
Lvl 5: Zeni x 35,000 --- D Medal x 15 --- Gear Bearing L --- Gear Bearing Z --- Refined Silver
lvl 6: Zeni x 55,000 --- D Medal x 15 --- Steel Nut L --- Steel Nut Z --- Refined Silver
Lvl 7: Zeni x 65,000 --- D Medal x 20 --- White Meteorite --- Refined Gold
Lvl 8: Zeni x 80,000 --- D Medal x 20 --- Black Meteorite --- Refined Gold
Lvl 9: Zeni x 95,000 --- D Medal x 25 --- White Meteorite --- Black Meteorite --- Refined Gold
Lvl 10: Zeni x 125,000 --- D Medal x 30 --- White Meteorite x 2 --- Black Meteorite x 2 --- Refined Gold
Lvl 10 Fight: You are up against 3 level 95 enemies. I personally chose to cheese the fight as Vegeta. Transform to Super Saiyan 2, spam Super Big Bang Attack (or whichever version you have) for ~700k damage (Vegeta Lvl 76) to any enemies in quite a large radius. The enemies can be really annoying, so bring some healing. Since you've spent 500,000 Zeni on building the room, you should be able to get some Healades or Senzu Beans.