This is a guide to summoned monsters of Final Fantasy V. In this game, the Summon ability works like any normal ability, with an animation just as long as any other, so it's nothing like summons in VII onwards (and certainly not like ones in X where you control the monster). Other than that there is an actual creature involved, summoning is different in the sense that summoned monsters are earned differently, and often have much more unique effects.
Generally, Summon magic is important. Not only do some summons deal heavy amounts of damage, but some have effects that can singlehandedly win boss battles. Summon Magic simply cannot overall be substituted for Blue Magic, White Magic or Black Magic. While several summons drop off later on, and are substituted in by much more powerful magic, the ultimate summons never drop off, and are always useful at some times at least.
There are no summons that are really worth missing, for achievements or not. One could make a good case for skipping Catoblepas, and as good as Leviathan is, one could argue it is not necessary, but in general, Summons shouldn't be skipped in any playthrough. Because they will be very useful.
Level One summons are the weakest by far. Not just for the obvious reason you're thinking, but for another reason; by the time a Summoner is worth using, these summons have already become useless in favour of the level 2 ones.
Like any level 1 summon, Chocobo is incredibly weak. By the time it is good to actually start using summoners, level 2 summons are already obtained. And Chocobo is not that strong. An offensive summon that can either do tons of damage as Fat Chocobo, or decent damage as Chocobo Kick, there is really no point in bothering. However, it is cheap, so there is no point in not buying it either.
Whisperwind - attacks an enemy then heals all party members for a quarter of the damage each
So of the level 1 summons, this is probably the most useful. It deals damage and gives all the damage back, splitting it between party members. Worked out the problem yet? The problem is that it barely deals any damage at all. Oh. Well, it has its uses as far as level 1 summons go, but it's hard to really talk about them when none of them are particularly good.
Worked out why this summon is a low level summon, the cheapest and costs almost no MP to use? Because it barely does anything. I'm not going to be too harsh to Remora, because for what it is, it's a decently useful summon to use in the earliest levels that has very useful effects in battle. But that's what it is, just a decently useful summon in the early levels when people don't use a lot of summoners.
Level Two summons follow the same theme of being elemental summons. They are the same elements that every Black Mage has anyway. This means that, as soon as Firaga, Blizzaga and Thundaga are lost, the level 2 summons are weak. Until then, they are very useful.
Ifrit is the first really good summon, and he is good for a while. Dealing fire damage to all enemies, at his level, Ifrit is great. While his damage will drop off, and Firaga will be used to replace him eventually, he's really not bad early on. Ifrit should, of course, be used against enemies weak to Fire damage and is helpful against bosses.
Ifrit is most likely the first summon you will unlock and not buy. However, you could also get Shiva, but you certainly should not get Shiva before buying Fira from Karnak. Funnily enough, whichever you get first will help defeat the other in a boss. The main reason Ifrit is most likely to unlock first is because he will automatically be unlocked as the story demands it, as soon as you get to the Library, and defeat him. Shiva, on the other hand, is more obscure.
Well known by fans of the series as the sexiest summon, Shiva is an ice damage dealing summon whose use is similar to that of Ifirit, but obviously, better used against enemies weak to Ice. In particular, Shiva comes in handy for one boss, Liquid Flame. She will eventually be replaced by Blizzaga in practical terms later on, but she is useful for the time she is around.
Shiva is found at the back of Castle Walse. If the player goes to the exit at the far right of the castle, goes around and out the exit to the back, they can face her and defeat her using Fira spam, and if they have it, Ifrit. Once they are unlocked, she is easy, but before that, she's a hard boss.
Judgement Bolt? Judgement Bolt?! WRAAHOOHOOHOOHOOHOOHOO FEEEEAR MY LIGHT OF JUDG-oh, it's Ramuh, not Kefka. BOO. Ahem. Ramuh, like the other level 2 summons, is an elemental summon that is great in the first few levels, but will ultimately be replaced by Thundaga. He exists to complete the elemental summon trio.
Ramuh is found in a normal random encounter either in a forest near Istory, or (apparently?) fought in the castle section of the Interdimensional Rift. He's a really easy boss and isn't too much trouble to deal with, you shouldn't have much of a problem. You're not really going out of your way to get this ok summon.
Level Three summons do not follow any particular theme. Only one is really weak, the thing is, that the one weak one I'm referring to is also the weakest and least reliable summon in the game. The other two are incredibly useful, one, in fact, can practically win several boss battles for you.
Golem is probably the most useful summon in the game. He may drop off later on, but his Earthen Wall protecting the party from physicals will be a literal lifesaver and can beat most bosses on its own. Golem renders any physical attacker useless for a while.
Golem is won in Drakenvale (and apparently the Rift?), during a fight. But he isn't defeated in the sense that the others are, rather, a fight where Golem is fighting two other enemies shows up. And Golem wins because you defeat the other two. I don't know if that's the case in the Rift, but it would make sense. However, getting him early is essential so I do not see why.
For a long while after he is obtained, Titan is the strongest damaging summon. Once obtained, there is almost no reason to use another summon offensively that isn't weakness to another element, resistance to earth, or floating. If the enemies are floating, earth will not hit. Titan is a very strong summon, and as there is no Black Magic for earth, probably the most reliable way of dealing damage of that element.
Titan is another boss that must be obtained for the story to progress, at Karnak Meteor. His boss is one of the two easier bosses of the meteors. It's fairly simple, and unlocks a really powerful summon.
Catoblepas is the weakest summon in the game, good against a single boss, and even then, there are alternatives. Catoblepas can instakill another boss, Carbuncle...problem is Bio Spellblade can also instakill it. His Demon Eye is random chance based and completely unreliable, and many bosses are immune to Petrify, making it even weaker.
Catoblepas is found on an island to the nortwhest of World Two, which can only be accessed once the submarine is unlocked. Accessed by diving, and entering a cave, then fighting up on the island above in the forest, he is a very hard boss. Every attack needs to hit really hard or else he will simply Petrify the whole party. I would almost argue that, other than for achievements, it's not worth even bothering to get it as going to the island it is on is too far out of the player's way to be worth it, but for Catoblepas, I make an exception since that island is also an excellent place to grind anyway.
Two of these follow a theme; the most powerful elemental summon, and of elements that only the Blue Mage can otherwise deal damage with. One that does not follow this theme is not particularly reliable, but not Catoblepas bad, while the other is Golem-esque useful. All but one are much harder bosses than previous summons, it must be said.
Incredibly easy to learn, Syldra is an awesome summon. Wind damage is very useful, especially since it cannot be used without Blue Mages otherwise. It's ironic that they called a wind spell "thunderstorm", but oh well. At the beginning of the third world, Syldra is the most powerful summon, and remains so for a while.
When entering the Pirate's Cove in the third world, simply entering the Hideout at the end of the dungeon plays a short scene where the spirit of Syldra, who wants to help Faris, returns and becomes a summonable monster. Aw, I missed Syldra.
Almost as useful as Golem, but not quite. Carbuncle places Reflect on the entire party. That means any attack that does not avoid Reflect no longer hits the party, it hits the enemy. Just imagine how useful that is against bosses which rely on magic. Spoiler: incredibly useful. Its main drawback is, once everything is reflected, healing, and positive status effects the party try to use on themselves, get reflected too. But that's a necessary balancing measure, as Carbuncle is otherwise very OP.
Carbuncle is unlocked in Castle Exdeath and is very hard to miss. However, he is ridiculously easy to defeat. Either Bio Spellblade once or a single summoning of Catoblepas can instantly defeat Carbuncle.
Ah, Odin, one of the coolest of all summons, but one of the most consistently useless. Odin has a chance to cause instant death to all enemies, but it's only a chance, and several enemies are immune to it. Those immune take damage from Gungnir, but there are better means of dealing damage. Odin's main use, however, is that he can make quick work of several bosses or groups of bosses. Any boss susceptible to Instant Death will probably die to it in one hit.
Odin is obtained in World Three. When the player enters Jachol Cave, goes through it, and comes out in the basement of Castle Bal, they will find Odin at the end. He is a relatively difficult boss for his level. Since it's not too much time to get it, there is little reason not to.
Leviathan's water damage is very useful. He essentially completes the elemental summons. Once unlocked, he can replace Syldra for enemies that are not otherwise weak to wind. Leviathan is a powerful summon, but very hard to obtain. His power does not completely substitute for his difficulty to learn. And after Leviathan, Bahamut will come. So it is entirely up to you whether you want to.
At the end of the Istory Falls dungeon, Leviathan appears as an optional boss. Due to how much damage he deals, a Coral Ring will probably come in handy for fighting him. No, four Coral Rings. Why buy such an expensive item four times for one boss? The only reason, other than achievements, I would give for actually bothering to put in that type of effort is because they are useful for another, even harder boss anyway.
The best two summons, for relatively obvious reasons. Once unlocked, one of these summons blows every offensive summon so far out of the water that there is literally not a single reason to ever use offensive summons again upon unlocking it. The other combines one of the best items with one of the best White Magic abilities, and Firaga. Both of these are exceptionally hard to get, to compensate for how good they are. But if you cannot get either of these summons, you have no hope against Exdeath.
Mega Flare - deals high non-elemental damage to all enemies
The be-all end-all offensive summon, Bahamut dualcast is probably the most powerful damage any mage can do. Once unlocked, you can replace almost every summon with Bahamut. I would normally argue other wise in cases of enemies weak to a certain element, but only Leviathan and Syldra should really be substituted, if the enemy is weak to Fire, Ice or something, by the time Bahamut is unlocked, just use Firaga Spellblade, seriously. Bahamut is a recurring summon throughout the series, and if he is not the strongest summon, he's always up there with the strongest.
Bahamut can be obtained after the first tablet is obtained from the Pyramid of Moore. Any point after that, going to the end of the North Mountain dungeon can initiate a fight with him. Bahamut is a ridiculously hard boss, the hardest to fight, but well worth it.
Flames of Rebirth - heals one character's MP and HP completely, and fire damage to all enemies
The de facto best defensive summon, Phoenix is practically an Elixir, but better. An Elixir and Arise in one, while also dealing decent damage, Phoenix is unquestionably amazing in tons of scenarios. There is literally no reason not to use Phoenix.
The Phoenix Tower dungeon may be difficult, but the reward at the end is sweet. There is no boss either. Phoenix is just awesome all around. Even if you want to skip Bahamut, there is no reason to skip Phoenix. Ever.