Rich Achievement Guide

How to get Rich Quick
Looking at the rich achievement and wondering how you can get that kind of money? Simple. The "tier" of an item determines its price. The tier of gear you find is determined by your characters level. Always have someone on your team with Decryption and Electronics. Do the minigame to open each container you find. Return to the citadel, and finish all side missions available before progressing the main storyline. Repeat this after finishing each of the four plot lines. Whenever you approach the 150 item cap, find a vendor and sell off all the lower tier items, and any items you are not using (no reason to carry around armor/guns/upgrades you are not using anyway). You will easily earn the Rich achievement. Earning this achievement unlocks the Elite prototype spectre gear. This gear is the highest damage/shots/accuracy for any weapon of an equivalent tier.

How to get Rich Quicker (albeit cheating)
Completing Citadel: Doctor Michel, opens the opportunity for you to earn an unlimited number of credits. Once Dr. Michel is safe, she will give you a better deal on the items she sells. Whether it is a bug or by design, this "better deal" extends to items that you sell to her, meaning that she'll buy equipment from you at a much higher price than other vendors.

To profit from this, simply sell her everything you can. You can then travel to another merchant on the Citadel, or even to the Requisitions Officer on the Normandy, and buy the last twenty items you sold for less than you sold them (I prefer Expat since he's right next to the Markets stop on the City Transit system, but any merchant will do.) You can then return to Dr. Michel and sell the items again, each time earning a profit.

While the amount you earn may be small at first, as you begin to sell the more expensive items, the profits increase dramatically. As your surplus cash increases, consider buying some of the higher-priced items from the other vendors on the Citadel. You'll lose money on the first round of trading, but ultimately you'll be making more money on each round with the more expensive items, which more than recoups the cost in the long run (and makes the process a heck of a lot faster.)

If you are uncomfortable with this degree of "cheating", it's still worth remembering that selling your items to Doctor Michel will always result in a greater profit than if you sell them to any other vendor. A good middle-ground might be simply to return to the Citadel whenever you are reaching the 150 item cap and selling all your excess to the Doctor. This will result in the greatest profit without resorting to any kind of arbitrage (or indeed "cheating.)

Personal Experience
On my first run-through, I followed the Party Member Achievement Guide, only I broke script after step 4 to return to the Citadel and use this method to better outfit my party. Thankfully, when you bring up the Sell dialog, for the most part it orders your inventory from least profitable to most profitable, allowing you to go to Dr. Michel and just sell everything in your inventory in order without worrying about which ones are worth the most. I then travelled to Expat and bought back everything I could (remember, it only allows you to buy the last twenty items, so if you end up selling cheaper items after your expensive ones, you'll end up losing the expensive items.) After a few cycles of this, I was able to start buying the expensive items from Expat's inventory, then Morlan downstairs, and eventually I worked the Spectre weapons into the mix. By the time I left the Citadel (about 45 minutes of repeating this process,) I had unlocked the Rich achievement, had purchased all of the Spectre weapons from both the C-Sec merchant and the Requisitions Officer on the Normandy, and had even managed to buy the Medical Exoskeleton VIII from Dr. Michel. This made completing the rest of the game a breeze.

How to get Rich slowly (albeit a bug)
There is a bug with the carry-over system for your character on the PC version, which duplicates any and ALL items in the current characters equipment screen. Before finish the final boss, equip the most expensive weapons, mods, armor and upgrades you have. Now, when you start the game again, use the "select an existing profile" option, and use your previous character. When the game starts, you character will be wearing the items from the previous run-through of the game, but upon opening up the equipment screen, there will be duplicate items of the equipped ones, including installed mods. Simply sell these items, and you gain, in essence, "free" money.

Personal experience
I'm not sure if the duplicate item big works on consoles, as i have only tried it on the PC version 1.0. It does require some effort, as you have to complete the game once to do it. The main advantage, is that with the duplicate items, you can equip your party members on the first level with high-grade weapons, which gives a huge advantage.