You need to earn a total of 450,000 cR across all modes to earn the rank of Lt. Colonel. You do not need to have the credits in the bank, it's a cumulative total.
To get the achievement you must purchase one of the following items that were unlocked by reaching this rank:
JFO Helmet - 60,000 cR
MJOLNIR Mk. V Helmet - 130,000 cR
CQC (left or right shoulder) - 20,000 cR
Collar/Breacher chest plate - 8,000 cR (credit Rhyolitic)
Tactical/UGPS (wrist) - 80,000 cR *also requires UA/Bracer (10,000 cR)
Black Visor - 100,000 cR
Grenadier knee guards - 45,000 cR
Here are the ranks to get to Lt. Colonel (the amount in parenthesis is how much cR is required to get to next rank):
Private - 7,500 cR (+2,500)
Corporal - 10,000 cR (+5,000)
Corporal Grade 1 - 15,000 cR (+5,000)
Sergeant - 20,000 cR (+6,250)
Sergeant Grade 1 - 26,250 cR (+6,250)
Sergeant Grade 2 - 32,500 cR (+12,500)
Warrant Officer - 45,000 cR (+33,000)
Warrant Officer Grade 1 - 78,000 cR (+33,000)
Warrant Officer Grade 2 - 111,000 cR (+33,000)
Warrant Officer Grade 3 - 144,000 cR (+66,000)
Captain - 210,000 cR (+23,000)
Captain Grade 1 - 233,000 cR (+23,000)
Captain Grade 2 - 256,000 cR (+23,000)
Captain Grade 3 - 279,000 cR (+46,000)
Major - 325,000 cR (+25,000)
Major Grade 1 - 350,000 cR (+25,000)
Major Grade 2 - 375,000 cR (+25,000)
Major Grade 3 - 400,000 cR (+50,000)
Lt. Colonel - 450,000 cR
cR earning tips:
-Playing gruntpocalypse on Corvette is rich in earning commendations which leads to consist cR bonuses (go to matchmaking, cooperative, score attack. keeping voting until you get corvette which is a small map). Without unlocking any major commendation levels, you can consistently average at least 1000 every 8-10 minutes clearing this just for all the double kills, triple kills, etc. When you do unlock a silver/gold commendation level you'll get a hefty bonus. Some games I was breaking 3000 cR.
-Playing sniper attack on Courtyard is also very rewarding with about 1000 cR each attempt. As soon as the level starts, cross the bridge in front of you, make a right and get to the end of this walkway. You can't be flanked from this position so it's a good place to camp out. If you're patient, most enemies will come at you in waves of 4 which will line up nicely for a one shot overkill. In wave 4 & 5, some enemies can jump or jetpack to your location so just be prepared for that. After a recent update you can no longer pick up enemy weapons in this mode. You will get a lot of multikills on this map. I was getting about 50 per attempt.
-Spamming the target locater on Oni Sword base. Start the level on Heroic and sprint along the right wall to get into the first base where the target locater is (don't kill anyone). Pick it up, get to the back corner on the same wall its located on to trigger a checkpoint. Kill the enemies with one shot, revert to last save over and over. It's been brought to my attention it's also useful to turn on the Thunderstorm skull to upgrade the types of enemies you are facing, so you work on even more commendations (credit MICKERR). You will get a lot of commendations to the silver/gold level this way and you will get a great amount of cR in 1 or 2 hours. Once most commendations reach gold, this method becomes less and less rewarding.
-Play Winter Contingency on Legendary with scoring on and safely sprint your way through the level without dying. When you get to the final room with the four grunts and the sword elite, save and quit. Now resume campaign progress and clear them out, push the button, and skip the cutscene. You should get a bonus commendation (200cR) for beating the level on legendary without dying (Flawless Cowboy). You can then resume campaign and you'll be back in that same room. You can do this about 25 times for a quick 5000+ cR. After that the time it takes to do this isn't worth the small cR in my opinion.
-Daily/Weekly Challenges: These are nice cR bonuses to take advantage of, and usually are fairly easy to obtain. To check what they are for a given day, press start, go to challenges. So far, most of the kills X amount of enemies in firefight matchmaking have been attainable while playing Gruntpocalypse which is nice.
-Play the MP & Campaign! It's a brilliant game, and you are rewarded with cR for doing nearly everything.
Update: You can now earn 100,000cR just by finding all the terminals in Halo CE: Anniversary and then going into Halo Waypoint and entering "secret" codes. See solution comments for more info. (credit Drummin003)
Note: 200,000 cR is the limit of credits you can earn in a day. (credit Quarantane)
Check out the guide by bl4ck blooc that shows an alternate way to unlock this achievement. It appears you can get the achievement done without actually reaching the rank of Lt. Colonel!
I will update this with more information, please post comments with other tips for the Reach community and I'll add them to this solution. I don't take credit for discovering any of these methods.