I can confirm that this achievement can be obtained in Solo Incursion ... It's just very difficult
The way I obtained it was:
Truth or Consequences - Downtown - Critical Difficulty
I can't remember which objectives I was assigned, but some of the tips I can give are:
1. Try getting objectives such as Sabotage, Serial Scanner and Shutdown; this is because the first two objectives, while being initiated, spawn more enemies, which increase the score; meanwhile, Shutdown, allows to take down nests multiple times, obviously before you place the foam injector.
2. Play with whichever operator you feel comfortable, i would personally recommend Level 10 Ela; your equipment must consist of the LMG (preferably both fire arms with suppressors), Paralysis Grenades and Recon Drone (Standard or XR ), this is so you can take down enemies such as Rooters, Tormentors, Smashers, (and maybe Sowers and Lurkers), and to paralyze Apex and have time to shoot them in the head, before they spawn more enemies; while using the drone to spot enemies and get few points for eliminating spotted enemies. Also if you run out of PG, don't forget to use Ela's Grzmot Mines, which get recharged one mine every minute.
3. Try getting High Bonus XP Parasite Mutations, such as Chimera Fog or Spontaneous Sludge. I wouldn't recommend going for Cloaked Archeans, because you will not be able to spot enemies (I mean you CAN spot them, with React Tech, but in my opinion that will make everything very difficult).
4. Try to be as sneaky as you can; spot weaker enemies (Grunts, Spikers, Breachers, and maybe even Sowers and Lurkers), shot their weak spot, then spot stronger enemies (Rooters, Tormentors, Smashers, Apex), eliminate this type of enemies by shooting their weak spot or with take downs, being stealthy or using PG; don't forget to spot nests and blinding spores, take down nests and eliminate blinding spores with the React Laser.
5. Don't forget that you are trying to farm as much points as you can; you are trying to reach At Least 29,000 points, before the bonus 90% for the Extraction (29,000*1.9=55,100).
I know it would be very difficult to get the 3 Objectives with any of the 2 Parasite Mutations I recommend, but just initiate an Incursion (Any Map of your Preference), Critical Difficult, check which objectives you got (Preferably Sabotage, Serial Scanner and Shutdown, any order is fine), with at least two of the three recommended objectives should be good enough; but if you don't get any of them, just initiate the incursion, and as soon as you spawn, call for Extraction.
I hope this helps any one trying to get this achievement, and forget me for any grammatical errors, since English is not my first language.