Whilst I'd advise doing Exploiter Orb in a group setting, it is possible to do it solo, albeit a bit tedious, as with the lack of speed and efficiency of a duo, trio or quad, you might find yourself taking a fair while combatting the Orb Mother.

Nevertheless, the Exploiter Orb isn't all to difficult, provided that you can get your head around shooting a thrown object. Phase 1 of the fight requires you to throw thermia canisters at the Orb Mother's frozen vents in order to expose them to be damaged. As such, you should consider what weapon might be ideal for you for this scenario.

Beyond that however, almost anything goes. I myself like to go for a more high-damage, speed-focused setup with Volt, with Zenith as my primary, Kuva Nukor as my secondary and a Zaw modded for Exodia Contagion as my melee.

I tried doing it with a group but either I can find anyone in the in game chat or there's a 10 min+ load time so people quit

Last time I was doing Exploiter runs I used Nezha for speed and tankiness, Trumna to shoot coolant raknoids, and tenet cycron to shoot the thermia canisters. Honestly you can use any heavy hitting primary for the raknoids, but for thermia canisters I suggest a highly accurate secondary because you don't have to swap weapons after throwing a canister and don't even have to adjust your aim. Any beam secondary is ideal for this, IMO. For her vulnerable phases outside I just hopped into a voidrig with a kuva grattler, which seemed pretty effective to me.