Archon hunts are harder than steel path. I would try to get comfortable in SP before worrying too much about archon hunts. The Fulmin, particularly a 7 forma Fulmin, should be fine for steel path. An upgrade if you like that style of weapon is the Tenet Arca Plasmor.

If you haven't done much SP, I also wonder if you're using weapon arcanes. Primary/Secondary Merciless are a pretty big step up in damage, so I'd start farming steel essense for arcane adapters if you haven't yet.

In terms of guns for Archons, the Zariman Incarnon guns (particularly the Felarx for the archons themselves, and the Laetum for regular mobs) are good choices. The Kuva Hek is another good gun for taking out Archons.

In terms of frames, someone that can stay alive easily like Revenant or Nezha can be a good way to ease yourself into it.

You might want to look into some armor strip if you want to do damage to the grineer more quickly. Unairu operator, Saryn, Mag, Necros, Hildryn, Ember, Vauban, Xaku are some that can do it without augments. If you have access to helminth you can put something like Necros terrify on anybody and you're good to go.

For survivability, you can use certain frames or look into shield gating(augur mods and/or brief respite). What can also help quite a bit is jumping and rolling around - makes it so fewer bullets hit you.

Warframe progression is a bit of a mess in my opinion, and really could use content gates to block off certain sections of the game until some minimum amount of progression is made before moving on.

*Make sure you are modding your weapons for the correct damage type. Archons are weakest to Radiation.

It seems like you don't even have access to Arbitrations yet which give you access to certain mods that make significant changes to how much damage your weapons can do as well as mods that help with your warframe's survivability. From Arbitrations, your priority would be to farm Adaptation for survivability or farm Vitus Essence to buy Rolling Guard (if you prefer Shield Gating, I personally don't find it a fun way to play but everyone is different) from the Arbitration Shop. (NPC can be found at the entrance of the Arbiters of Hexis area of a relay). The Mods you need to farm Vitus Essence for would be Galvanized Chamber (split chamber may be slightly better for certain bosses like Eidolons) and Galvanized Shot which is the mod that will give you the largest increase in damage if you're able to inflict some status effects on enemies. Just remember to prioritize your preferred weapon's equivalents, Galvanized Mods are broken up into Rifle, Shotgun, and Pistol, don't waste Essence on the Shotgun mods if you do not plan on using a Shotgun. Mods like Galvanized Scope/crosshairs I would rate as very low priority.

Next you can try either some Steel Path content with the Daily Incursions, or work on finding a weapon that is suitable for fighting lvl 150 enemies. I would recommend a Kuva Hek for this because Archons because of how strong it is and how it interacts with Damage Attenuation. Many hits in one shot are better than one large hit from a sniper. Also avoid using the Perigale for bosses if you are a client. Although its gimmick looks like it would be great for bosses, it does not function correctly if you are playing as a client and will run out of ammo extremely fast.

For a good general purpose frame, Wisp kind of a "jack of all trades" frame. Health and Haste motes are great for support, and Breach Surge if you need some crowd control and some extra damage. Shock motes are not always the best, and may even be a hinderance in Defense missions, or to Harrows trying to get their buffs. Unless I see an objective taking significant amounts of damage (or if I need a little more survivability) I tend to avoid placing down shock motes. Wisp Prime is coming out soon, you're better off waiting for her release and farming her then, than you are building a base Wisp from scratch. (You can ignore the Arcanes I have on my Wisp build, energize is nice but not mandatory for anything, and Pistoleer is entirely useless for Archons)

Other notable weapons would be the Felarx and Laetum from the Zaramin.

Usually the most dangerous things in an Archon fight are the enemies, not the boss; especially the Sentients when they start doing their "disco ball" attack. If you can't kill them quickly find something to block Line of Sight between you and the attack until its finished.

Archon Hunts are the most difficult content available right now. If you don't do enough damage you're simply not ready to solo them. It's a fact you have to learn to accept.

It's not your fault though, so don't take it as a personal attack or anything. Warframe progression is completely stupid and often throws at you content you're not ready for. Take open worlds for example. A new player has no way to handle PoE but the game sends you there when you're like MR3. Archon Hunts are the same.

To make matters worse, Archons have a rather unique defence mechanism to them which makes most weapons and abilities useless.

So, from where you're standing right now, you have 2 options.

1. Get the Zariman weapons or Kuva Hek. Mod them for Radiation damage and pair them with Ivara or other stealth frame of your choice. Ivara provides additional damage boosting options though, so she's the best for Archon Hunts. Give her Roar with as high strength and duration as you can and Rolling Guard for survivability. That's all you need.

2. Don't try to solo it and ask for help. I understand you don't want to feel like a leech and want to be useful but you don't have to rely on damage alone to do that. Remember, Archon Hunts have perma death, so having someone who can heal, boost, and revive, is actually super useful there. I'm running a Vazarin Harrow Prime with Roar for support and it's great. Damage buff, CC, CC buff, immortality, fast revives, all in one package.

You need a fair amount of skill and gear to solo archon missions. They're pretty hard. Don't be afraid to ask for help.

Somethings you may want to grind for the gear to do them more easily:

-Arbitrations: (clear every node on regular star chart to unlock) A lot of good mods for higher level builds such as Galvanized weapon mods, Rolling Guard and Adaptation. Some mods from the mission, some come from the Arbitors of Hexis shop (does not require arbitor rep).

-Zariman: (Angels of Zariman quest) Grind up the faction rep and buy good weapons(Laetum, Phenmor) and good arcanes.

-Duviri stuff: Some of the Incarnon weapon variants are very good from SP Circuit. Reg Circuit can get you new frames and augment mods. Also other loot like new arcanes come from circuit filler loot or can be bought from the resource shop if you do the free roam missions.

-Lich/Sisters: Kuva Hek is a popular choice, but the 1 hit kill build is fiddly and takes some power house mods you might not have without doing other stuff first. Radiation is generally the best choice for Archons so check the progenitor list to correctly spawn a lich with the desired element base.

https://warframe.fandom.com/wiki/Lich_System/Progenitor

There's a lot of good weapons for various things from Liches/Sisters.

-Helminth Uprades: (Deimos) Get the upgrade segments for your Helminth so you can mulch warframes. Every frame as 1 power that can be learned by mulching which can then be used on other frames. Xata's Whisper (Xaku) and Roar (Rhino) are big DPS boosting powers and really useful for Archon hunting.

Play circuit, get op incarnon weapon, delete steel path enemies. That or fight kuva liches to get kuva weapons. You can also play kahl missions after veilbreaker, they are fun. Also, try new frames, get better mods, play arbitration. A lot of stuff gets unlocked after you unlock steel path...

Archon Hunts are roughly equivalent to mid-tier Steel Path.

The Fulmins kind of so so (magazine is a bit small and the recharge takes a bit) at dealing with them. But a Hunter Munitions build should work. The Fulmin itself isn't great at the viral so a primer would go well.

The Archons themselves can be attritioned with nearly anything (even Operator), though there are speedier builds out there for them (though the absolute fastest require everyone else not to shoot the Archon or it gets messed up)

As far as the frame survivability goes, would have to know what frame and maybe some of the build.

First, I recommend not spending Plat on basic items and frames. But you do you.

Second, Steel Path it where you get some of the gear you need to do the "Hard Mode" stuff. (See 'Primary/Secondary Merciless')

SP is easier than Archon Hunts. So no worries.

Zariman, get Phenmor, melt Archons. You really cant get wrong with Zariman weapons from Cavalero. They are easy to get, no RNG involved, you just play missions there, get materials, and rep, and boom you have solid end-game weapons. Alternatives for Zariman weapons are Kuva/Tennet weapons, or some rare Primes, or godroll Rivens. So Zariman weapons are easiest way to get one of the best weapons in the game.

Comparing to older content Zariman doesnt have that much grind at all. You just work towards unlocking stuff and thats all, really easy and simple. Almost no RNG involved apart from getting initial bank of Entrati Lantenrs, but eventually you will have them enough, just by doing missions.

Laetus - melts everything Phenmor/Felarx - melts everything, and best Archon hunter Praedos - my to go Acolyte farmer in SP with super easy and cheap heavy attack build

And best parts about Leatum and Phenmor - they are early in reputation, so like few days worth of reputation from 0 and you have both. Laetum is actually 0 rep requirements, Phenmor is 1st or 2nd rep level

Or you can always equip Hirudo on Inaros and cheese them that way. Inaros with Hirudo is "press one button and win pretty much every content while watching Netflix", except Arbitration, because pure melee not that good vs Arbitration drones xD You need some ranged weapon to kill Arbitration drones effectively

Take an unkillable frame, like Revenant, inaros, wukong, nezha... I only started using revenant on the assassination mission for the last two runs (with xaku's ability) and I'm surprised I never used him before for this. He will never die if you keep mesmer skin up.

Fulmin should be ok for most mobs but need to be able to kill heavily armoured mobs. I haven't used the Fulmin in a long time, but maybe a build based on hunter munitions and slash will work. Hunter munitions drops from ghoul purge bounties in Plains of Eidolon.

Final boss will probably need something like kuva hek, or I prefer the felarx. When I started, I used mostly the zariman incarnon weapons for the assassination. Since you can't take the fulmin, will also need a decent secondary or melee to deal with most mobs. Again, incarnon secondary weapons are really good for this. I used the laetum before, but now I use the Lex Prime with incarnon.

To be honest i wouldn't bother about archon hunts yet. I think when it was released, we already had access to the original incarnon weapons, which made it a lot easier.

For the easiest frame option in terms of resources/time to acquire:

Step 1: Get Revenant (Prime, which should be easy to acquire)

Step 2: Get Natural Talent (the mod)

Step 3: Slap Natural Talent and ability strength into Revenant, also energy economy

Step 4: Congratz, you are now immortal with Revenant's 2.

For the best weapons:

Felarx, Laetum, Phenmor with Devouring Attrition (the incarnon perk that gives a 50% chance on a non-crit for 2000% damage, which bypasses damage adaptation that Archons have, and will kill anything below an Archon quite easily)

For the easy weapons:

I can't be of much help since I mainly use the Felarx, but any weapon with multishot and tons of tiny damage instances instead of one big one should do. Shotguns work well for this, provided they're pellet shotguns and not big blasts like the Arca Plasmor.

Well I cannot add much that what other already told you. This game is hard to play if you lock yourself into one build. I guess the fullmin could work with some armor shredding helminth?