Meeting the Grim Reaper?

Personally, I don't know of any way other than having someone, human or animal, die. If you want to, just for the achievements, you can perhaps get a mod that allows you to kill other sims and you can just off random townies to get him to come. That's what I'd do personally, you can always remove the mod afterwards.

You could have a scientist sim make the ghost serum. If the sim doesn't turn into ghost, Grim Reaper comes to slap them.
Or you could get one death flower from the gallery. Then a sim dies, you'll save them, befriend the Grim Reaper, and nobody dies.

Death Flowers I have. Each of my family members is currently carrying 2 Perfect Death Flowers. Slim chance any of them will ever die in the first place. Every one of them is a Vampire and thus immune to death by old age or hunger (since they don't age and Vampire Thirst isn't fatal). On top of that, the Teen and both parents have the Naturalist Reward Trait from the Freelance Botanist Aspiration, further rendering them immune to death by fire. They're virtually unkillable. I could switch to a mortal family for the Achievement but that doesn't help my Vampires with the Grilled Cheese Aspiration goal, which says to "Talk to the Grim Reaper about Grilled Cheese".

Maybe hang around elder townies and wait for them to die? That's what I do when I have an aspiration that requires interacting with grim and nobody in my vicinity is going to be dying any time soon.

By pure chance, I found a small, noninvasive mod that can help with this. It's called Book of Chaos. I found out about it while watching a Sims 4 video by Call Me Kevin on YouTube. It puts a Book of Chaos into Buy Mode that lets me kill whoever I want. I just killed off a Townie I never particularly liked, the Grim Reaper showed up and, thanks to my Incredibly Friendly Reward Trait, befriended Grimmy with a single introduction, netting me the Hello Darkness Achievement instantly.

I officially love the Book of Chaos. I finally got the ultimate revenge! I've had a vendetta against the Landgraabs since what Malcolm did in Sims 1 and Bustin' Out on GameCube. Malcolm and Jeffrey are now dead and it's a much-needed victory. Down with the Landgraab Empire! :P

Congrats on the Hello Darkness Achievement!

If anyone else is looking for a way to summon the Grim Reaper without a mod, in addition to kalaksed's excellent suggestions, you could also go into CAS to make a disposable Sim and temporarily move them into your house to kill them. It's an alternative for people who have populated their town with their own Sims and/or don't have any townies they're okay with killing.

There's always the pool without a ladder deal (except you'll need to build walls after getting the sim in the pool), then electrocution -- make a tv break then get a less-than-capable sim to "fix" it, after getting shocked once. There's a cowplant (right? does that need expansions...?), and then there's also supposedly extreme emotions, but I've never gotten that one. According to a guide, it's Anger, Embarrassment, Overexertion (elders only so nvm), and Hysteria (laughter). Good luck! Or not >:)

I also forgot to mention that I expect you'll be using your death flowers. But there are specific emotions your sim can be in to plead/flirt(flirty)/demand(confident) the life be spared.

True, there are other methods for sparing a Sim from the Reaper, but... Death Flowers are one of only two methods known to be guaranteed to work every time. The other ways, there's always a chance of being denied. The better your relationship with the Grim Reaper, the better your odds of success, but with the social methods, there's still always even the tiniest chance of refusal.