What's the best way to get the "Rampage!" achievement?
Solution 1:
I'd suggest playing easy bots and being more sneaky than usual. I got this achievement on my 2nd try versus easy bots on the Baggage level. First off, I stuck to the outside of the map (right side from CT spawn ramp) and peaked bots to kill them and retreated when necessary. Definitely do not go running around the middle of the map, try not to get shot even once because your health needs to last the entire match.
It is very possible to go a long while without getting shot once versus easy bots. My first try I had gotten shot once for 13 damage all the way until nearly the end when some bot got lucky and killed me.
The last kill with the knife was pretty tricky... The bots all had shotguns at that point and it was difficult to get close enough to kill one without getting shot. I would recommend going down the ramp from CT maybe into the lower baggage area and try to find one that isn't looking. Be Very sneaky when trying to get the final knife kill, the knife kill may take a few tries.
If you wanna do this versus humans you're just going to have to be VERY good and get lucky by playing against some weaker opponents. I really think that against humans this is nearly impossible. Stick to easy bots. (If you want to cheese it, bots_knives_only will probably get you an easy win, but you said you wanted it legitimately)
Solution 2:
I'd recommend having only 1 enemy and 2 allied bots; (bot_kick )
With this setup your allied bots will find and distract the enemy, possibly lowering his health, while you go in for the actual kill.
Solution 3:
Ok, Easiest and quickest way to get Rampage with no cheats is on Safehouse. Seriously, with a good line up of weapons, it's easy for me to finish Safehouse with very few deaths. So enough tries, you'll get it. A successful attempt will only take between 5-10 minutes.
Join Terrorist side and stand in the doorway to the bathroom at the top of the stairs. You get a great vantage point looking down the stairs at the front door. At that range, even short shotguns will not be a problem when it comes to just slaughtering easy bots as they come through the front door or try to go up the stairs. You don't have to venture from that spot really. You do have to keep an eye on the doorway to the Bombsite room though. If you get into trouble, just pull back into the bathroom and chill for a bit.
When it comes time for that knife kill, just wait in that bathroom for someone to come upstairs, preferably when some of your teammates are there to distract them, run out and knife 'em.
If that's not a good enough explanation, here's a video: