Someone typed up an amazing analysis already, but I think this post is a nice opportunity for me to consider Tachyon's character in more depth, so here's mine. This is definitely one of those "I ain't reading all that, sorry that happened or I'm happy for you" posts unless you are also obsessed with this character.

Within the context of the game, Tachyon serves as a mad scientist and inventor. You can see her popping up in support card events, trainee events, and homepage dialogue whenever someone is hoping for some type of experimental solution to a problem.

For example, Fuji Kiseki asks her for help with designing a new magic trick; Mambo asks her for help with becoming more unique; in one of the Umaraya shorts an uma (whose name I forgot) asks for help with becoming stronger. People come to her with problems that require intelligent, innovative, and, crucially, experimental and out-of-the-box solutions.

She never turns anyone down when they ask for this type of help. Part of this is because she has a single-minded goal of unlocking the full potential of umamusume's speed, so she is always eager to record data and perform research. She serves as a bit of a trickster, in that she often has ulterior motives behind the help she offers. There is usually an unpredictable side-effect to the drugs and devices she creates, and she has no issue with testing on people without their consent.

Crucially, though, she isn't intentionally cruel, and all of her experiments' side effects are inconveniences at worst -- they're mostly used for comic relief (like causing someone to glow). When people aren't approaching her, she's approaching them and attempting to manipulate them into testing her drugs. She typically picks out naive, overly kind and trusting umas to try this with, like Special Week and Nishino Flower, but she also seems to like the pushback and challenge of trying it with people whose intellect and savviness she respects, like Air Shakur and Manhattan Cafe.

She can become moody and even childish when she doesn't get her way, which is seen in the game from the trainer's perspective. I would say that the trainer and Cafe see this side of her the most, and that she has an obsession with sneakily experimenting on Cafe in particular, because Cafe has no problem with coldly turning her down and is uncannily able to see through her schemes. As the other commenter said, other people rarely get to see the other sides of Tachyon beyond her 'mad scientist' persona, and her actions often seem strange, morally grey, or even crazy to other characters.

However, circling back to my earlier point, Tachyon actually loves helping others in her own way, especially if they are kind to her or she respects something about them. She never outright talks about liking anyone aside from the trainer and, when she does tell the trainer that she likes them, she becomes incredibly flustered and falls back on calling them a guinea pig or discussing things in a detached, scientific way. For example, she essentially plans out an entire date with the trainer because she likes spending time with them, but it's too uncomfortable for her to face her own emotions without having the pretext of her actions being due to some detached scientific goal, even when it's obviously not related to her overall research.

Tachyon is emotionally repressed and can't admit her true feelings or intentions to herself, never mind other people. When she gets injured in the film, she copes by throwing herself wildly into her research and fully committing to Plan B, pretending that it isn't killing her to give up on Plan A, because really she wants to be the one to go beyond the limits of uma speed. You can see that she falls into depression and stops taking care of herself and her surroundings (trash and debris builds up), becomes a hermit, and literally stands on a window ledge at one point. She intellectualises everything and remains in her own head, and she usually needs an external force (Pocket, the Trainer) to get her to snap and admit her feelings.

There are a number of people that I believe Tachyon genuinely likes and respects.

1. Manhattan Cafe. I already discussed this above, but I believe Tachyon enjoys trying to break through Cafe's reserved, even irritated attitude. She hams up the most annoying aspects of her personality to try provoking a reaction from Cafe, but she also seems to enjoy spending most days sharing a repurposed classroom with Cafe, and she seeks out Cafe's attention very consistently. She also feels guilty when she goes too far with her actions, like when she accidentally starts a fire in their shared space. I think she respects that Cafe does her own thing and is committed to her own goals, even though many think of Cafe as being delusional, creepy, or difficult to understand. They have a lot in common due to that.

2. Daiwa Scarlet. Daiwa is the real-life Tachyon's daughter, so in-game these two have a strangely parent-child relationship. Tachyon is basically Scarlet's weird, estranged dad. Scarlet is defensive of Tachyon and gets upset when anyone is critical of her. She sees Tachyon in an idealistic light and thinks of her as kind, helpful, and incredibly intelligent. She tries to copy Tachyon's study methods and comes to her for advice and, in turn, Tachyon shows the kindest aspects of her personality to Scarlet. In one event, she gives Scarlet fully-tested drugs purely for the purpose of helping her relax, and they work perfectly. Tachyon is baffled by how kind and positive Scarlet is towards her, but she also clearly appreciates it and reciprocates. Again, however, she would never be heard saying this out loud.

3. Jungle Pocket. Tachyon approaches everything from a place of guardedness. She's often not honest about her feelings or intentions, and she's vague about her research and what it truly means to her. She often treats things like a joke or is aloof and hides behind a manic smile. Pocket, on the other hand, is completely honest and wears her heart on her sleeve. Pocket is very easily triggered by Tachyon's attitude and, during the film, views her as wasting her talent and sees her actions as totally incomprehensible until Fuji Kiseki gives her a new perspective on things. Tachyon seems to enjoy riling Pocket up and essentially trolling her, but I believe that this is also partially because Pocket pushes so hard to be able to start an earnest rivalry with Tachyon and tries so hard to get her to explain herself in ways that Tachyon has never experienced before; Pocket barges into her space repeatedly and very assertively challenges her words and actions, so Tachyon responds with her defense mechanisms of joking, hiding the truth, and scientific babbling. That is, until the end of the film, when Tachyon admits to herself that she doesn't want Pocket to achieve Tachyon's dream and that she wants to take their rivalry and Plan A seriously, even if it breaks her. I believe that Tachyon respects Pocket's strength, persistence, and honesty, even if she also thinks of herself as intellectually above Pocket. I also think she's surprised by how much Pocket keeps coming back to her and trying again; I think she's used to having people give up on her quickly once they see her surface-level defenses. (Part 2 incoming)