I've tried to lure him into the lava with my reapers with 30 seconds before the next flow, but he always scampers back to his little corner right before it comes up. What's the best way to kill him with lava?
I built supply depots at the bottom of the ramp, and made them sink into the ground. Then I created a line of marines for him to kill, like a cookie trail for him to follow, then told them all to "stop" (so they wouldn't move). With about 50 seconds left, I sent a single reaper to lure the brutalisk to my cookie-trail of marines. When he got below the ramp, I put the supply depots back up.
The lava doesn't kill him right away, but the marines damaged him enough that he died before he could make it back.
It took me a while to figure this out, but when I did it was pretty easy. My solution is a variation of the bunker trick mentioned in another answer.
First of all, kill the other units around the brutalisk. This shouldn't be too hard, and you don't want them getting in your way.
Float a command center (with SCV's loaded in it) down to the expansion just to the right of the brutalisk. You could just run some SCVs there, but the CC makes this solution a little more elegant. Using this back entrance is better than the front entrance is better because you don't have to lure the brutalisk for as great a distance.
Build a bunker in the expansion, and use a marine to lure the brutalisk to the bunker. You don't have to worry about the timing too much, because you can use SCVs to repair the bunker, effectively keeping the brutalisk tied up indefinitely. (Just use a single marine, because you don't want to accidentally kill the brutalisk.)
Just before the lava rises, have the CC load up the SCVs and lift off. You'll lose the bunker and one marine, but everything else will survive. And as a bonus, you have your next base to mine from!
I ran an SCV and some brave, loyal Marines down to the Brutalisk's hideout with a few minutes until lava flow. The SCV built a bunker relatively near the ramp, and a couple Marines loaded up. With about 30 seconds to go, I used a single Marine to lure the Brutalisk back to the Bunker trap.
Luring him up to the Bunker was actually kind of difficult, and I probably should have brought a couple Marines along and given myself more time; it's easy for him to walk back away from you if he loses sight and you don't shoot enough, and it's also easy to lose your Marine. It took me two tries to successfully pull him into the trap.
Once the other Marines in the Bunker started shooting at the Brutalisk, his fate was sealed. In a blood rage, he charged the Bunker and took a few ineffectual swipes. Then lava arrived and everything erupted in a blaze of glory. Achievement unlocked.
I first tried luring him out into the big open field in front of the starting base, but I always seemed to lose his attention. I think he doesn't want to stray to far away from his starting area.
I later just brought him to a small mineral patch to the Brutalisk right and just did circles around the small area until the lava rose and all my units died (with him included). If you are looking to keep units alive, maybe use reapers so as to jump up the cliff at the last moment.
Tip: The best approach to luring is to not lose sight of him and take a few shots every so often.
Here's a decent YouTube video that I followed.
The narrator walks you through it. The great part is you do this with your starting SCVs and marines so that if you don't get it the first time, it's easy to try again.
This achievement is all about the timing. You will lose the Brutalisk's attention quickly once he's on the lower level.
This is really simple.
Just follow Plikt's answer up to the Command Centre (CC) and then lift.
The stupid Brutalisk has an anti-air attack and, upon seeing a lifted-off CC, will follow it and attempt to destroy it...
Oh, did I mention that CCs can pick up SCVs while floating in mid air as well as drop them off? So...
Lure with a SCV to the area to the Brutalisk's right = Pick up in your FLOATING CC = watch as said Brutalisk crisps as it pointlessly shoots your CC (after all, you probably are collecting mineral ore in that area anyway.) while swimming in lava.
WHat I did was save my game just before luring him out. I also finished collecting all other achievements before so Even if i sacrificed my whole army, it was ok(since im not going to finish the map anyway...or just kill it last)
Anyway, at 20 seconds before the lava flow, just go with a group of marines and marauders(the brutalisk can take a beating from the lava, it's not a one hit KO) and rain some bullets upon it. run towards the ground and keep shooting and running to coax it out. at about 3-5 seconds left, it should already be out in the open and killing your marines. Then just wait for the lava to engulf you both.
Don't forget to give those heroes a good funeral :P They will always be remembered
What I did is I took a few reapers (4), and when there was about 15 seconds left, I attacked with the reapers, and did a typical reaper harass with it (attack, run, repeat), while luring it to the east ramp. There's a little "bay" there, and they walked into the bay, and then hopped up the cliff on the northwest part of the bay as the brutalisk was getting near, and the lava got him.
It's not that hard actually... I started looked around, and read about like thousand of different techniques. I finally do it myself with a Reaper and [recorded a video] (it's not that hard actually).
Hope it helps :)
EDIT: I just realized I can't post the link to youtube here, searching by this...
Starcraft II Devil's Playground - Red Lobster Achievement
...in youtube should be enough, the user also has my real name that you can get from the stackexchange profile.