I finally unlocked this achievement after watching the Rooster Teeth's Achievement Hunter video for this, so my tactics were very similar. Since I don't recall hearing the video mention any of the difficulty/skull details, I completed this achievement on Normal difficulty, with the Catch, Sugar Cookies, and Rebel Sympathizer skulls activated. One note before beginning: right before completing the mission, right after getting the achievement, I received the 100/100 Grunts killed notice. However, there were still more Grunts alive inside the base the I killed after receiving this notice. I'm not sure what to make of this, but I am wondering if there are actually more than 100 Grunts in the level.
After many tries, I finally unlocked this achievement (just about five minutes ago, actually). For the first few Grunts/groups of Grunts, I used non-Forge, regular Warthogs to get the kills, pulling guerrilla hit-and-run tactics, trying to allow my Ram ability to recharge (aided by the Catch skull) while minimizing non-Ram damage taken by the Grunts. Most of the time, I tried to use one or maybe two Warthogs at a time, as precision-controlling multiple Warthogs while trying to not allow the trigger-happy gunners to tear too many Grunts to bits can be a challenge. After my Warthogs took too much damage or were destroyed, I allowed Forge to take over. While his Gauss cannon makes short work of Grunts, controlling one 'Hog is arguably easier than controlling a group. Hit-and-run is the key here. The only time I would recommend killing the Grunts as quickly as possible, with little regard to running and allowing Ram to recharge, is when non-controllable Marines are fighting them. Here, you are essentially on a short timer with no control over the Marines and their killing.
Along the way to Alpha Base, do not underestimate the value of the lone Grunt or two. I ended up getting this achievement with about 5-10 Grunts left, but luckily, after watching the video, the value of every single Grunt really occurred to me. When given the choice of the group of Grunts versus the lone Grunt, however, the choice is clear - always maximize your effectiveness and run down the group!
Once you're outside Alpha Base, use a couple squads of Marines to down the barrier, then move everybody back as far as you can from the base. I led everybody except Forge down to near the level's Black Box, but as long as they are out of range of the base entrance, you should be fine. Before you first enter Alpha Base with Forge (or whichever Warthog(s) you choose to use), scout out the enemy. Here, you have a choice: you could either aim for the highest concentration of Grunts for the first strike, or you could aim for the groups nearest the Wraiths, which will most likely be taken out by the ensuing air strike. If you get lucky, one group fits into both categories, choose them as your first target. After you make your first strike, run outside of the base to allow Ram to recharge. After the air strike has gone off, the game is simple: hit-and-run. Always scout ahead before each hit, targeting the largest Grunt groups (preferably the ones in the middle of the base, as the ones behind the pelicans/on the outskirts will stay there), and possibly even behind them to maximize your Ram's effectiveness. While enemies may follow you out of the base, always keep the greatest distance possible between yourself and the enemy unless you're making a Ram hit. After all enemies from the middle of the base are cleared out, use similar hit-and-run tactics for the remaining, stationary outskirt enemies.
Finally, don't get discouraged. I tried for this achievement many times, many ways before finally unlocking it. To those who say it is easy, I'm glad you feel that way. Maybe you caught a lucky break :) To those who call it the hardest in the game, I have yet to get all the achievements in this game, but it certainly took more effort than many of the others. Keep trying, and if my solution doesn't work for you, you may just have to take a different route. The longer it takes, the sweeter it feels to finally see "Achievement unlocked 5G - Everything's Better With Bacon".
I have also embedded Rooster Teeth's Achievement Hunter video here in this solution. Good luck!