Having originally been developed for the more traditional CBS Network before moving to The CW, Supergirl has retained a slightly different approach to its storytelling than the other DC Extended Universe TV shows in the so-called "Arrowverse" continuity. Kara Danver's adventures have used personal stories and character relationships as fodder for long-term narrative arcs while villains, while the more conventional superhero fare plays out more as episode-to-episode distractions (until it doesn't.) As such, it can be difficult (largely by design) to predict which of the various villains or villainous forces will end up being the big challenge superhero TV seasons typically build up to.
After all, few would've predicted at the start of season 1 that Non and Indigo would wind up as the big bads after so much of the actual season had centered on the machinations of Astra? Likewise, season 2 has built the vast majority of Kara's challenges around Lillian Luthor and CADMUS... only to throw a curveball over the last few episodes with the arrival of Mon-El's unfriendly alien parents (Teri Hatcher and Kevin Sorbo) as a potentially more dangerous threat, with a personal vendetta and a cache of kryptonite weaponry to boot. And there's still the unknown motivations of the secretly-alien President Marston.
But with season 2 heading into its home stretch, the list of (known) candidates seems to be coalescing. Let's look at who the most likely suspects are (in no particular order):
LILLIAN LUTHOR
The leader of CADMUS has been the featured nemesis for most of Season 2, even longer than we've known that she actually is Lillian Luthor (aka Lex's mom) so it makes sense that she'd remain so right up to the end. Along with the ever-present influence of tradition (i.e. she's a Luthor), she makes the most sense as the "big boss" of the season for more thematic reasons. Season 2 is where Supergirl staked out its overriding ideological claim on being a show about immigration, and as the leader of the anti-alien hate group CADMUS (think The Minutemen, but they hate space-aliens instead of Latinos) she's the face of the opposition. On the other hand, maybe the fact that it's so obvious means that won't be the case...
QUEEN RHEA
Longtime DC fans guessed the "surprise twist" that supposed Daxamite refugee Mon-El was actually the Crown Prince of the planet's royal family almost immediately, but few were expecting his parents to have also survived and come looking for him as a late-season plot swerve. Teri Hatcher falls neatly into a very specific "sweet spot" for Supergirl casting i.e. a fondly-remembered former TV/film star best known for association with a prior DC/Superman project giving a slightly campy supporting turn (see also: Dean Cain, Helen Slater, Lynda Carter), and her performance as Rhea has marked a welcome return for the sort of vamping "wicked witch" female villain that was Supergirl's stock-in-trade for season 1 but hasn't featured as prominently in season 2. More practically, her character certainly "feels like" the biggest possible threat: She's got a personal vendetta, her own giant spaceship, an army of henchmen, a pair of Kryptonite-edged daggers (with apparently more where that came from) a strength comparable to Kara's.
PRESIDENT MARSDIN
It's probably always going to feel (true or not) like Supergirl had a different set of plans for Lynda Carter's Olivia Marsdin: Casting the former Wonder Woman as a fictional first female President and having her personally charge Kara and the DEO with aiding in an aggressively pro-amnesty (for alien immigrants like Kara) policy push felt from the start like the series was gearing up to explore where it's proudly-feminist heroine would "fit" in what was expected to be the era of a similarly feminist President Hillary Clinton. That's not how things worked out, of course, and it's now unclear if the new reality has changed any of those plans - including whether or not Marsdin was ultimately meant to be a good guy or a villain.
Fans have known since her debut that Marsdin has a secret: She's actually an alien shape-shifter herself. Since she only just recently showed back up as a physical presence in the series, her broader agenda (assuming she has one - she certainly wouldn't "need" additional reasons to conceal her identity beyond the obvious ones) has remained a mystery. Storywise, it would make sense as a "shocking twist" for Kara to have to confront an ally and personal hero turning out to have been on the "right" side for a nefarious reason: Supergirl loves to revisit the idea of Kara's relative optimism as her "real" kryptonite, and it nicely upends the moral-binary between the DEO and CADMUS.
It's very possible this was the plan all along, but with Supergirl showing no sign of backing away from it's velvet-glove political engagement (see: Sorbo's authoritarian King Lar Gand unctuously boasting his aim to "Make Daxam great again!") it's worth wondering whether the producers would still want to "complicate" their overriding pro-immigrant running themes in an era where the threat of border walls, travel bans and anti-immigrant hate crimes are part of the daily news cycle.
LENA LUTHOR
It's a running theme in the DC Universe that Luthors and the House of El are essentially fated to end up as enemies (on Earth 3, where Kal-El is evil and called "Ultra Man," Lex was Earth's greatest hero) but Supergirl likes to play around with its own mythos and the expectations thereof: While Lex Luthor has already been exposed as a supervillain, defeated by Superman and imprisoned prior to the events of Season 1, Lena Luthor's life goal is to prove she's nothing like her infamous relatives... or, at least, that's what she says.
Lena as a "surprise" ultimate villain makes a lot of sense, thematically: It would be an emotional gut-punch for the series' fanbase, which has proven so fond of the character and her chemistry with Melissa Benoist's Kara that there's an entire sub-fandom dedicated to the idea of them as prospective romantic partners. It would be an appropriately dark turn, given her apparently sincere desire to be the "good Luthor" and the wrench that was thrown into that by the revelation that, while Lillian Luthor is indeed her mother and she was adopted... she is Lex's actual biological half-sister. More broadly, it would serve as a "dark side" mirror to one of season 2's other big storylines i.e. Mon-El also being a villain's offspring trying to redirect his fate.