I will not be very elaborate when discussing matchups. If you want to know more about certain matchups, or would like to discuss them, check out the Matchup Modern series on the Spirits subreddit! I get most of my information from this page, but alter some things I don't agree with or see slightly differently from personal experience. I want to give a shoutout to TheRift who is active on both the subreddit and discord, and who's comments on the Matchup Monday threads were of great help to me.
Humans
Humans has been known as a bad matchup for spirits for a long time. This is because Humans is a creatures aggro deck, against which cards like Mausoleum Wanderer are just less effective. Spirits tend to not have the greatest stats anyway, so creature aggro has been a real problem. However, with the "new" addition of Supreme Phantom, this matchup has not been as bad for spirits anymore. Both Bant and UW have been able to put winrates up to 60% with reasonable sample sizes. The reason why this matchup has gotten so much better, is because what goes for spirits, also goes for humans. With this I mean that card like Mausoleum Wanderer, Thalia, Guardian of Thraben, and Spell Queller could be a less effective, but Humans' Kitesail Freebooter, Meddling Mage, Reflector Mage, and Thalia, Guardian of Thraben are all bad against spirits. Furthermore, as I touched upon earlier, Supreme Phantom buffs all our creatures, while also being a very good blocker itself. Spirits can swarm just as well as Humans, and Humans' strong top end in Mantis Rider is easily stopped by all our flying creatures.
So, what was once a terrible matchup has sprung into our favour. Spirits used to be called a worse version of Humans. Spirits' big 3-drops might be a little slow against Humans, I would advise cutting a number or Spell Quellers and Drogskol Captains, while also cutting Thalia, Guardian of Thraben. Some great cards in the sideboard against Humans are Echoing Truth, Settle the Wreckage, and Worship.
Tron
Another matchup most people think is very bad for us. However, I believe the matchup is pretty close, but most likely still in Tron's favour. Spirits is a tempo deck, which means we really put a clock on what Tron wants to do. Furthermore, cards like Oblivion Stone, Wurmcoil Engine are bad against spirits, even Karn Liberated is not great. We have Selfless Spirit to blank Oblivion Stone. Path to Exile, Nebelgast Herald, and Phantasmal Image are great against Wurmcoil Engine, pretty good against Ulamog, the Ceaseless Hunger as well. Karn Liberated's -3 gets stopped by Rattlechains, and killed of easily afterwards. That all being said, it is very easy to misplay against Tron. Spell Quellering the wrong spell, not attacking when you should, sacrificing Selfless Spirit when its not optimal, all these decisions can win or lose you the game easily against Tron. And beware of Ugin, the Spirit Dragon. If that resolves, we just straight up lose the game due to its -X ability.
As for sideboarding, Aether Vial is not great, since we will be bringing in Stony Silence. Other than that, Unified Will is great, and Echoing Truth is ok.
UWx Control
Control is a good matchups for Spirits. Nearly all our creatures answer theirs in some form or another. UWx control plays few creatures, and a lot of non-creatures. This means that Mausoleum Wanderer, Thalia, Guardian of Thraben, Drogskol Captain, Rattlechains, and Spell Queller are all very good. We are not pressured into a tempo gameplan, but can very well win the game before UWx control can do anything. Furthermore, counterspells are not great against Aether Vial. Removal gets blanked by Rattlechains and Spell Queller, and board wipes like Wrath of God get stopped by Selfless Spirit. A lot of UWx control list are running multiple copies of Terminus, which we can't stop with Spell Queller and Selfless Spirit, so they are not completely hopeless against us. Nevertheless, Spirits definitely has the upper hand.
When going into sideboarding, I think Spirits is very well equiped to beat UWx control post sideboard. Eidolon of Rhetoric, Kira, Great Glass-Spinner, Remorseful Cleric, Rest in Peace, Vendilion Clique, and Unified Will can be good options dependent on what kind of control deck it is. Path to Exile is pretty bad, but you might want to keep 1 or 2 in for any Celestial Colonnade, or a sideboard Baneslayer Angel. Be careful not to over-sideboard in this matchup.
Hollow One
Now this is a really bad matchup. Before sideboarding, Spirits will often lose the first game. The reason for this is that Hollow one is extremely fast, and extremely disruptive. Discarding 3 cards at random because of Burning Inquiry makes playing the game very difficult. However, there is a chance you can win. A turn 1 Mausoleum Wanderer might buy you some time, as it can counter their first discard spell, or at least delay it. Nebelgast Herald is also an important card, as it can tap a Hollow One to buy some time. You should not make unfavourable trades if at all possible, I think that the best strategy to use here is going broader and bigger than what Hollow one tries to do. Getting multiple lords is necessary. If you can get a good draw and achieve this, you can definitely win the game.
The sideboard is very important here. you should probably bring in Remorseful Cleric, Rest in Peace, Echoing Truth, and Eidolon of Rhetoric as they all stop or delay Hollow one's gameplan. Since its all about speed in this matchup. Spell Queller can probably be trimmed, and perhaps also the Phantasmal Images.
Burn
Burn can be a difficult matchup, but both sides can win if they draw well. Aether Vial is an important card in this matchup, as it allows us to play around Eidolon of the Great Revel. If you can't find an Aether Vial or Path to Exile, and they drop the eidolon, it might turn out to be a difficult game. However, Spirits has some ways to play around eidolon. You can try to Spell Queller it, if you can find the mana, and Phantasmal Image is great when copying Eidolon of the Great Revel, since eidolon is a spirit. If you effectively force 2 Eidolon of the Great Revels onto the field, one of them getting buffed by our lords, and can play around them using Aether Vial, we are in a pretty good spot. Finally, you can try to fake your opponent out by leaving the board empty. If they attack with Eidolon of the Great Revel, any flash creature we might have trades with it. Goblin Guide is not a big problem for Spirits, as we trade easily with it. Monastery Swiftspear is a bit of a problem, the high toughness in combination with the prowess triggers makes it so we cant trade with it easily. As such, this is a great target for Path to Exile. Grim Lavamancer is also scary, you just have to get a couple of lords out on the field, or Path to Exile it. Supreme Phantom is a nice card against Grim Lavamancer, as it buffs our creatures, and is outside the range of lavamancer. If the Burn player has to target your creatures with burn spells like Lightning Bolt, you're in a pretty decent spot. Try to get them into such a scenario.
I would board Blessed Alliance, Eidolon of Rhetoric and perhaps Echoing Truth in, while boarding out Nebelgast Herald, and maybe another couple of 3 drops. Burn has a lot of artifact hate in the sideboard, so bringing out the Aether Vials in certain scenario's can aslos be a good idea.
Bridgevine
Bridgevine is a very tricky matchup for a lot of decks, this one included. We can definitely fight them head on, and win a lot of games. However, if they get an insane start on turn 1, you will most likely lose the game. Otherwise, this deck runs a few creatures that can just block zombies all day, and this deck runs some creatures that can sacrifice themselves, exiling any Bridge from Belows in your opponents graveyard. Path to Exiles are important cards, and the main target you want to use them on are Viscera Seer and Vengevine. When playing against this deck, luck (or lack thereof for your opponent) and speed are very important. For that reason, the slowest pieces in this deck should get cut when sideboarding.
Spell Queller hits almost nothing, and is relatively slow. It can block zombies, but I don't consider it worth playing it. Aether Vial is too slow/unimpactful in such a matchup. Further options for cutting are Drogskol Captain and Nebelgast Herald. As for what cards we board in after game 1, Rest in Peace and Remorseful Cleric are obvious inclusions. Echoing Truth and maybe Worship can also be great.
Storm
Storm is one of the best matchups for Spirits. Storm generally doesn't like aggro, and it also does not like disruption. Spirits are these two combined. Mausoleum Wanderer can counter a lot of set-up spells, sometimes even the first ritual if that means they can't do anything else that turn. You should often play around Mausoleum Wanderer when playing against storm. Meaning that you should leave flash creatures in hand a little longer, just to get that P/T boost for Mausoleum Wanderer. Wanderer is also a great creature to copy with Phantasmal Image. Spell Queller hits everything Storm runs. The spells you want to counter most of the time with Spell Queller or any other counters you might have are Baral, Chief of Compliance, Goblin Electromancer, Gifts Ungiven, and Past in Flames.
Eidolon of Rhetoric, Unified Will, and Rest in Peace are all solid answers to what storm tries to do. I usually cut Selfless Spirit and Nebelgast Herald, although if you feel your creature density is going down too much, cutting 2 Aether Vials is also fine.
Mirror & Bant Spirits
When facing UW or Bant spirits, you've got to keep in mind that they are an aggro-control deck, and sideboard accordingly. UW's Nebelgast Herald is great in both mirrors, while
collective company
is great for Bant. Spell Queller is an all-star for both versions, important spells to counter are Collected Company, Nebelgast Herald, Drogskol Captain, and sideboard cards like Worship and Settle the Wreckage. Rattlechains are also important, as flashing in an extra creature might put you in a very good position, on top of killing your opponents Phantasmal Image if it copied a spirit. The sideboard is very important in this matchup.
Worship, Echoing Truth, and Settle the Wreckage are all great options, but your opponent might have them as well, while Thalia, Guardian of Thraben is a little sub-par.
Death's Shadow
Death's shadow is a deck with a lot of 50/50 matchups. However, I think Spirits has the upper hand. Death's shadow want to get to a low life total and then beat you down with big creatures, while controlling your hand and the board. However, Death's shadow has trouble dealing with the sheer number of creatures Spirits can get down, and due to the evasion, Spirits can punish low life totals heavily. Mausoleum Wanderer has many targets to hit, if your hand is great, countering a Thoughtseize might be worth it, while countering removal is great as well. This is also a matchup where Thalia, Guardian of Thraben and Nebelgast Herald shine.
A lot of sideboard card can have a big impact in this matchup. Eidolon of Rhetoric is nice since Death's shadow usually runs lots of cheap cantrips and other spells to assemble the win. Echoing Truth is great against delve creatures. Blessed Alliance can shrink your opponents Death's Shadow, while also letting your opponent sacrifice creatures, as Death's shadow usually attacks with a couple big threats. Unified Will, Remorseful Cleric and Rest in Peace are great sideboard options as well.