This is an outdated post, the new tier list can be found here:
Smash Ultimate Amiibo Tier List – American
This post was written two weeks ahead of time. Please consider that recent developments in the vanilla metagame have not been taken into account because of that delay.

Send all hate mail to donttakethisseriously@gmail.com.
This tier list is organized out of vanilla, and has a bit of a foundation in the current tournament tracker. (You can find it at this link, by the way). I also organized this list with the best representations of that amiibo in mind: if every Ike I’ve ever seen was absolutely awful except for this one specific one, then I pegged Ike based on that amiibo. Unlike my Smash 4 tier lists, this one isn’t based on the game theory aspect of amiibo: we don’t know who counters what yet, so there’s no game theory to speak of. Instead, I’m basing this off of the maximum known potential of an amiibo. One single trainer absolutely can make a difference.
Before I explain this list, I’d like to make note of a few circumstances surrounding this tier list. First, it’s a little over a month into the meta. We have just shy of 70 characters to try out across two types of tournaments, and the tournament tracker has very stringent requirements for what they accept as tournament results. The meta’s a mess right now, which is why amiibo training is so fun: you never know how things will turn out.
Also, this is clearly not a comprehensive list. There’s going to be characters left out of this that will end up in these tiers, and some that are already in these tiers that I just plain forgot about. Once we get to a more absolute tier list the tiers will be much larger than 4-6 characters each.
I’ll go through the tiers and explain what they mean, and then some of the individual spots.

Glitched: If Olimar isn’t banned from a tournament, he’s S tier. However, he benefits from a glitch that increases his damage and knockback output. While it’ s more prevalent in Spirits because of the larger multiplier, the glitch still affects the 20% improvement for amiibo. Without the glitch, we don’t know how well he’d do.
S tier: Voted Most Likely to Succeed in high school, this tier contains the amiibo most likely to… succeed. If you’re putting money on an amiibo character to win, these are your best picks. Bear in mind they’re no much better than A+, and A+ isn’t much better than A, and so on. S tier isn’t head and shoulders above the tier below it unlike most metagames with tier lists.
A+ tier: These amiibo still win tournaments and do so quite well. It’s a fair bet to say they have more potential, but nobody’s unlocked that yet so they’ll be down here for a while. These amiibo are worth putting time into.
A tier: Like A+ tier, these amiibo can do well if somebody would show them a little love. Some of them may never break out of this tier, but most of them eventually will.
B tier: At least you’re not lower.
Unfamiliar: I put this tier here because I’m not familiar with these amiibo enough to place them. They either don’t have much recent representation, I haven’t trained them, or the data says they’ve done well in the past but I haven’t seen them perform ever. This tier is separate from the rest because I simply don’t know.
Let’s go down the list and explain what we can, shall we?

Link: Link is the best option in vanilla right now… kinda. Lucina can beat Link if she’s got Learning Off, and Link benefits a lot more from the usual stages than most amiibo. I’ve gone into detail previously about how Final Destination and Battlefield benefits Link more than other characters, and as long as tournaments focus on those stages alone he’ll have a very, very strong foothold in the meta. Recent tournaments have shown that his grip is weakening, fortunately, but the best Links are the best amiibo overall.
Lucina: Beats Link and most A+ tiers handily because of her affinity for forward smashes. MiDe’s Lucina (also known as Shadowrift in the ASMR #1 bracket) is one to keep an eye on, and I used that amiibo as the example of Lucina’s potential.
Zelda: Tico’s Zelda is the example for this one. Zelda performs well against Link, particularly in her offstage play. Link can throw out projectiles easily, but Zelda seems to know how to dodge them well. She also has kill options at short range immediately out of short hop, and her side special can cover a chunk of most stages, and KO at medium percents.
Mii Gunner: I expect to be dragged over the coals for this. I’m fine with that, because I’ve seen a Mii Gunner that will knock your socks off.
In ASMR #2, Vintro submitted a Mii Gunner that was the definition of a perfect amiibo: he never made a mistake. He didn’t jump until absolutely necessary, he used the best close-range moves possible, and laid down the perfect projectile spam. The fact that Ganondorf took even one game off of this Gunner is a testament to Ganondorf’s creativity, not Mii Gunner’s. I strongly suspect there’s a training method somewhere in there that nobody else knows about yet.
ROB: I think he just handles himself well. In much the same way that ROB was a good vanilla amiibo in Smash 4 without any particular strengths, he’s just kinda really good in Ultimate too. There’s nothing special about him except that he’s good.

Young Link: Some people have problems keeping their Young Link from SDing. I haven’t seen those people. Every Young Link I’ve seen fought with great intelligence, even going so far as to almost take a set off my Link in ASMR #1. That Link ended up winning the tournament, too. The Young Link was submitted by myriad_truth, which is the one I used as the example.
Bowser: Dude’s big. He’s got so much potential it seems unfair to leave him out of S tier, but save for Vintro’s Round Robin #0 I have yet to witness any stellar results from this character.

Mii Swordfighter: This is my amiibo main, and I’m the only trainer I know of who does Swordfighter. My Mii has taken 4th or better in every tournament he’s entered except for one, where he was eliminated by an Olimar (who we now know to have a glitched advantage). I count that as a pretty solid reason to include him on these upper echelons.
Ike: Ike benefits from his character more than his AI, as he is well-suited for heavy-hitting aerial combat. Now that we’re in a metagame that prioritizes air-ground fluidity and early KOs, Ike has improved drastically compared to Smash 4. I don’t have any Ikes in particular that I’m using as an example for this, his position on this tier list is based solely off of tournament rankings.

Ganondorf: If you win a tournament with Ganondorf, buy a lottery ticket. If you lose a tournament, consider buying one anyway. Those are both pretty rare outcomes for Ganondorf.
Ganon is a pretty inconsistent amiibo, but never inconsistent enough to produce results definitely towards victory or failure. I’ve seen Ganons make it up to Grand Finals (like ASMR #2) and I’ve seen those same Ganons get eliminated in the first round. Magic’s Ganon is my example of a good Ganondorf: he’s the one who almost won in ASMR #2. It pains me as a Ganondorf main to see the embodiment of the incredible girth of my personality do so poorly compared to his Smash 4 appearance, but that only means I’ll have to train him harder.

Yoshi: Some people think Yoshi is a good amiibo. I believe those people, but I’ve never seen one in action. Yoshi hasn’t yet been submitted to a tournament that I’ve watched, and as of recent I haven’t seen very good results from him. I’ll have to watch a good Yoshi in action before I fall in line with the prevailing opinions.
Donkey Kong: He’s in the same situation as Yoshi.

Isabelle: Isabelle might be the first amiibo that has been pushed to her absolute maximum, and she’ll probably be the only one for a while. Hidari’s Isabelle is my example of an Isabelle, and it’s a very good one. In ASMR #2, his Isabelle took a set off of a Link, only to be annihilated by the Mii Gunner that won the tournament. If you read the guest post by Hidari two weeks ago, you’ll be able to see just how deep the rabbit hole of Isabelle’s training goes.
Pikachu: Also in the same boat as Yoshi. I’ve heard of Pikachus doing very well, and I’m well aware of Pikachu’s massive buffs in Ultimate that lend themselves to amiibo play. I haven’t seen any of them in action and nobody talks about Pikachu much. I’ll have to see him for myself.
Greninja: This may be the only placement that I disagree with every time I see my list. I’ve trained a Greninja and I can’t imagine that he’d be in B tier, but the spreadsheet indicates that he’s running a win percent in the 60s, which puts him in the higher tiers. Data overrides me on this one.
Little Mac: Mac should be good in vanilla due to his one-hit KO punch, but he’s not. Now that amiibo are less horrible in the air, Little Mac leaves much to be desired. What little footage I’ve seen of him indicates that he’s not completely worthless, in fact thanks to his raw power he might be able to do some good, but I can’t imagine that he’d ever get to S tier in vanilla.

Cloud: Much of the reason Cloud was so dominant in Smash 4 was his character’s overwhelming superiority over everyone not named Bayonetta. That carried over to Smash 4’s amiibo game, where he was one of two characters restricted for use in customs tournaments.
In Ultimate, he’s been thoroughly nerfed. His sword is now a toothpick with a green trail, his limit activates but goes away after 15 seconds and he’s not faster than anyone else thanks to Ultimate’s speed buffs. While I haven’t seen much tournament footage of Cloud, my own Cloud amiibo seems to be coming along quite nicely and should at least be a contender for moderate tournament placings as training methods develop.
Conclusion
You’ve probably found a number of inconsistencies between your own personal opinions and this tier list. Hell, I have too. That’s the way it should be, because we’re only a month into Ultimate at this point and we haven’t even gathered data on every character available to us. This tier list is obviously going to be different in the future, so when you dig up this old one and snicker at it, just remember where you started.