Her first moves are going to be crushing, throwing, and trying to mangle Regulus with her TK. When Regulus isn't bothered at all by these things, she'll probably use the environment. When that doesn't work, she'll look towards throwing him into space.
Regulus has an authority which lets him ignore Tatsumaki's defenses and throw things at FTL, but Tatsumaki is fast enough to aim dodge pretty much everything. Regulus usually holds back a lot and doesn't try so much to kill the opponent. He was struggling to hit Subaru, who could also aim dodge things. Tatsumaki is much faster with much more mobility. She should be capable of the same for some time as he yaps.
If Regulus manages to hit her a single time, she dies. No real argument there.
Tatsumaki has a much harder time actually doing anything to Regulus. It's possible she could sense the abnormalities within Regulus' body and connect that to his Lion's Heart. She has a TK ability which seemingly allows her to sense metaphysical connections like that, since she was able to find Psykos' real body from Gyoro practically instantly.
The probability of this happening in the fight seems low, but it is possible. If she connected those things, she could definitely win through destroying the heart that is latched onto his wives and then fighting Regulus with the time limit restraint.
Though, it is much more likely Regulus gets serious and kills her before that happens.
Otherwise, she could try BFR. This is way more in-character and requires less assumptions. The issue is that she only tried this once, at the END of a fight that lasted quite some time.
By that point, Regulus could have already just said "no" to being moved around by TK, though... which is a very effective counter.
Overall, Regulus just has a way easier time winning this one. I have to make a lot of assumptions on Tatsumaki's behalf to even come up with solid win-conditions. I do not have to do this when discussing Regulus.
