Warframe

Sorties are daily events that refresh at noon EST. You must be Mastery Rank 4 and using a level 30 Warframe. Three random mission types, the first at level 50-60, then 60-80, and finally 80-100. The details of how sorties work are best left to the wiki.

http://warframe.wikia.com/wiki/Sortie

To paraphrase the important bits, ciphers cannot be used and endless modes have finite caps; 10 waves of a mobile operative for defense, 15 minute survival, 3 waves of interception, 1000 base cryotic. Each stage has a modifier to make it harder. Completing the entire sortie for a day and getting a reward from the table counts as one sortie complete.

SOLO RUNS
It is absolutely possible to solo sorties, though the difficulty is highly dependent on which missions are drawn. Endless missions and assassinations will prove tricky for the majority of players, and it is not recommended to solo these.

Additionally, the modifiers can cause problems if the mission is normally easy. Energy Reduction is a big one, as it cuts your energy to a quarter and similarly slashes the regen rate of Energy Siphon and Zenurik's pulse, which can be a wake-up call if you find yourself relying on permastealth Loki. Similarly, Eximus Stronghold will spawn more Energy Leech Eximus and can quickly drain you - the further on in the sortie this shows up, the more problematic it is.

THE KING AND QUEEN WARFRAMES
I've soloed sorties as well as played with one extra player, and I've gotten on just fine with two frames: Loki and Nyx. Naturally, the Prime versions are superior, but these have since been vaulted.

Loki
The permastealth build is listed in many solutions for a reason: once enemies can't see you, running through most objective missions is a breeze.
Aura: Energy Siphon
Efficiency: Streamline and Fleeting Expertise, both level 4/5
Duration: Continuity and Constitution maxed, Narrow Minded at level 7 or more.
Optional: Hushed Invisibility lifts the primary restriction against weapons by making every weapon silent. Coaction Drift increases

The goal is to make Invisibility cost as little as possible (12.5 energy) and generate 13 or more energy in that timeframe. For a solo player without Coaction Drift, Invisibility has to last 21.6 seconds - with Coaction Drift, 18.6 seconds.

Nyx
Nyx is the crowd control frame for a very good reason. With range and efficiency maxed out, Chaos and Absorb cover a very large area and can shut down points with ease. Chaos irradiates everything within a 60m radius (!) and gets enemies to fight themselves, while Absorb can be used to sit on a defense point and quickly toggled on and off to knock over enemies repeatedly with a 23.5m shockwave.

OTHER GREAT WARFRAMES
Any of these frames I'd only recommend in certain instances, and definitely not solo. Once again, if a Prime version exists, it's clearly superior, but not necessary.

Nova
Excellent on endless points with Molecular Prime, max out duration so the bubble expands for longer. Enemies are slowed down scaled to power strength and explode when killed. Ideal especially on Interception and Defense.

Frost/Vauban
Another good one for Interception, Survival, and Mobile Defense. Frost with the Chilling Globe augment has a chance to freeze enemies entering the shield, where Vauban with the Repelling Bastille augment can push enemies away from a target. Both fill the same role on a team, but since the Defense target moves around, they're less useful there.

Limbo
The king of distraction. Beefed up duration can result in a 60+ second Rift Walk - you can't hurt them, but they can't hurt you... but they can still see and target you, taking fire off teammates or letting you revive them with ease. Just keep in mind you can't interact with things while in the rift.

Nezha
This is technically cheating - Nezha is a sortie reward, and if you're lucky, you'll get his parts at the same time as this achievement. However, those parts are tradeable and obtainable beforehand. Nezha is a jack of all trades who can heal with Blazing Chakram and, with his augment Safeguard, Warding Halo can be cast on allies as a weak equivalent of Iron Skin, but importantly protects them from status effects.

STATUS MODS AND YOU
As the enemies are such high leveled, damage is not nearly as important as crowd control - their level doesn't matter if they can't hit you. Getting the right status effects on enemies will give you a much easier time, so focus on weapons with high status chance and mod them to 100%.

Route 1: Dual Stat
Each weapon type has four mods of 60% elemental damage and 60% status chance, one for each element. They are found as follows:
Heat/Cold: Spy missions. All three vaults must be successfully hacked to get a chance at these. Melee mods are found in spy missions between Earth and Ceres, Cold-Rifle and Heat-Shotgun are on Jupiter, Europa, Saturn, and Lua, and everything else is found from Uranus onwards.
Electricity: Event only. Baro Ki'teer occasionally sells them, but only appears every two weeks and may not have the mods.
Toxin: Corrupted Vor in the Void. Vor will spawn in Void missions above level 40 and will drop one of the four mods each time.

Route 2: Multishot
Multishot adds a percentage chance to fire two rounds at once with no change in ammo consumption. Getting Multishot up and over 100% will double your status chance by sheer volume. This has no use on melee, naturally.

The primary mods are Split Chamber for rifles, Hell's Chamber for shotguns, and Barrel Diffusion for secondary. These are possible rewards for high level endless missions, defined as anything on Uranus and onwards. Secondaries also have the alert-only mod Lethal Torrent, which increases multishot and fire rate.

HIGH STATUS WEAPONS
Compiling a list of weapons, as some of the modifiers limit the weapons you can bring. These are suggestions based on status chance and elements; this is not a definitive list of greatness. Event weapons and vaulted weapons are excluded, but Primes are fair game.

I'll include the status percentage first, plus any notes I feel are important.

ASSAULT RIFLES
Braton Prime - 20%, my preferred option, very solid rifle
Grakata - 20%, very ammo inefficient
Burston Prime Prime - 15%, burst fire, possible syndicate weapon through Arbiters

SHOTGUNS
Hek - 25%, able to get 200% multishot solely out of Scattered Justice, highly recommended
Boar - 20%, full auto shotgun
Tigris Prime - 30%, pure damage
Sancti Tigris - 25%, easier to get than Tigris Prime, syndicate radial explosion

SNIPERS
Vectis - 30%, single shot magazine, excellent use of Charged Chamber
Any sniper will do, just don't expect to actually use it.

BOWS
Mutalist Cernos - 45%, fires its own toxin projectile, can easily leave gas clouds everywhere
Dread - 20%, high base crit chance can be built above 100% crit chance, major slash damage
Paris Prime - 20%, the puncture equivalent of Dread

SECONDARY/PISTOL
Pox - 35%, creates toxin clouds, my preferred secondary when built with Toxin, Gas, or Viral
Vaykor Marelok - 35%, mini rifle in secondary, syndicate weapon, excellent choice
Synoid Gammacor - 20%, not as strong as it was, still an excellent choice for Corpus

MELEE
Lesion - 30%, easy to get to 100%, passive ability increases attack speed and toxin damage on status effect, highly recommended
Lacera - 45%, base electricity damage, great range