2 Star Gaming did a video on this a long time ago, pre-Eximus rework. Not sure how well it works with the new Eximus units, they may have done a follow-up video, I'm not sure.
The Excavation mission can be cheesed with Limbo, but it's really really boring. As far as I'm aware, you don't have to actually complete any excavators, just get a certain amount of Cryotic. So just run around as Limbo in the Rift, activate the Excavators, and let them get blown up for a small amount of Cryotic. Rinse and repeat, watching out for Eximus units that can hit you through the Rift. Maybe subsume Banshee's Silence if that's a problem for you: while it's active, Eximus can't cast their abilities that hit through the Rift, and Silence itself works across the Rift.
For the other two, there's a little known trick. The game says that all mods are disabled, but that's not entirely true. Warframe Augment mods still work for some reason. So the strategy is: grab Hildryn, subsume Chroma's Elemental Ward over her 1 or 4, and make sure your Emissive colour gives you Electric Ward (Purple colours usually work for this). Then, equip Hildryn's Blazing Pillage mod. Activate Elemental Ward, activate Haven, and start spamming Pillage. The combination of Pillage's armour/shield strip, Haven and Blazing Pillage's heat damage, and Elemental Ward's interaction with Hildryn is enough to shred the mobs at the level of Grendel's missions. Just keep an eye out for Eximus units, as their Overguard is the biggest unknown since it didn't exist when I did this strat.
Finally, don't be afraid to ask for help in Recruit chat! Only the mission's host needs to have a Grendel locator to access the mission, iirc, and plenty of players will jump at the chance to farm Grendel in a group, or at least get a second copy to subsume to the Helminth.
I farmed Grendel again recently because I needed the subsume ability and both times I used the hildryn method and it still worked.
It is possible to skip adding elemental ward, just will be killing things a bit slower. Important now if the player is new, I think I saw this week duviri curcuit was hildryn and could get the haven augment mod with it.
I did bring a hammer this time in anticipation of eximus units being too tough to kill and some were. I don't remember being in danger of getting killed though.
But bloody hell this mission can be a bore at 20 min survival or the 800 cryotic excavation that barely spawns the right mobs to charge the excavator.
Hello, I have soloed the Grendel Missions multiple times in the past, and I can tell you the easiest and most accessible way to do them is just one word. Garuda
This applies to all the missions, just use Garuda and the rest of your loadout really doesnt matter. Just make sure your Garuda is Rank 30 with no Mods Equipped so you start off with Max Energy
To explain why its this, it comes down to pure Synergy. Garuda is a deadly Warframe on its own, her 4 Will be able to mass stagger if not outright kill most of the Enemies, her 2 will allow you to Keep Alive in any situation as her Healing Scales with how much health you're missing while also allowing you to use your 3 to Refill your energy on Demand, her 1 is a Neat Survavibility Tool but since youre using your 4 which gives Invencibility it instead becomes a Nuker, use her 1 and Let Enemies shoot at the Shield, when a Tanky Unit like an Eximus appears, using her 4 in Combination with throwing her 1 is a Death Sentence regardless of Enemy Level
As of the explabation, there is a strategy to be maintained here, yoy must keep her 2 Active and Constantly use your 3 and 4. BUT if you have access to the Helminth System and Sevagoth subsumed, give her Bloom instead of her 2 and you can Play the Mission without a care in the world, her Ability's Damage will heal you
If specters/equipment can be used, they can be really helpful too (wiki doesn't say mention if gear wheel is disabled). Something like a wisp specter provides some CC and some healing to the objective and will last the full 10 rounds. A railjack specter will probably despawn before the end of the mission but they don't cost anything to craft, and can be helpful with trying to keep the Defense objective alive.
As for frames, Wisp, Xaku, Octavia, Hildryn or Nekros (Ivara should be fine for survival and comes with a looting ability for life support so might be worth it to run there with melee/weapons that are silent by default like the Baza) would probably be my choices for frames that should do okay without mods. Grab any augments you like because they still function in the Grendel missions.
If power cells are really an issue in excavation, just spawn a new excavator and let the old one die assuming the mission is total cryotic and not n-excavators completed. Preferably though, you would be playing Nekros here for the extra canister drops.