Truly solo? As in, I put down only one ship and attempt to table the enemy? As others have said, a lot of these ships have pretty decent counters. A quad TLT list could ruin the day of most of the ships that can do this, but aside from Soontir (general consensus and worlds proves that he can do this), I wouldn't mind the flying any of the following:

Super Dash (in this setup, he NEEDS Kanan over Kyle, the unpredictability beats the focus if you are against a full squad)

Corran (PTL, EU, FCS, R2-D2)

Poe (although he would probably need PTL over VI in this situation to be able to boost and focus)

Miranda could do well.

I guess ultimately the main requirements are some kind of arc dodging ability, the ability to put out at least three attack dice, and (ideally) some regen. So my money is on Corran.

Ships that can solo ships that can solo an entire list:

Carnor Jax

Was going to say this as well. He is my favourite squint and has now become even more popular with the triple toilet seat builds.

I've been playing Carnor with PTL,RGT,AT,SD and Dark Curse together a lot lately and have only lost 1 game. Only time I lost carnor was the game I lost. All other games he cleaned up pretty much on his own. Dark Curse with SD and having a focus token has proven to be quite hard to take down for my opponents but only 1 of my builds has this - the one where the 3rd ship is Whisper with VI,ACD,FCS,Reb Captive.

Soontir would have to be flown perfectly.

Psycho Tycho can (and did for me several times last year) solo numerous lists. Pretty much any list that moved before him he could solo. This includes Dash + Corran (when Tycho does NOT have the init), along with 7 TIE swarms (though 8 TIE would be the same outcome), 4 TLTs, BBBBZ... And I'm sure other things - but those I have solo'd with just him. (Note, when I say solo, I don't mean that I literally plopped down a 38pt Tycho and that's it, I mean that I lost Corran and the Prototype in the opening exchange and Tycho killed all 100pts of the opponent afterwards).

When you can come from outside of R3 to within R1 and out of arc in a single turn, it's very difficult to lock him down and get a shot if you move first. The combo of boost/DD and a full dial means that he can go where you can't block him, and can navigate such that no one gets a shot (and the rare case where that's not possible, F+E for the single attack coming through prevents all damage... most of the time).

Given, it's going to take awhile. I spent over 3 hours killing a 7 TIE swarm with Tycho... and I did lose 2 shields in the process. But those were early on in the engagement. Once it got down to 4 TIEs, I don't think a single shot was fired on him.

I once soloed a full-health PS10 Corran Horn, and 9HP PS9 Dash Rendar, with a PS8 IG88-B in an elimination match. It's not something that can happen very often though.

It's not something that can happen very often though.

Well, it's always possible. .