Trish was tearing through dozens of demons with the Sparda sword. Once she had dispatched with them, she felt hot breath on the back of her neck. She spun around to see a large, red and black dinosaur-looking demon (a fiend, in actuality) a little bigger than the purple ones Lady had encountered on the night she met Trish. She jumped back and was about to attack when out of nowhere, she looked up to see a blonde girl with her hair jump out from nowhere, going right for the monster with a massive black and red war hammer with spikes on the other side of the crushing side, effortlessly smash the monster's head like it was nothing.
"Fiends. No matter how many of them you kill, they just never stop coming." The girl said, lifting the massive hammer like nothing and swinging it lightly to get the blood off of it, before she noticed Trish off to her side and looked slightly surprised, stepping back and looking like she was guarding an attack. "Who are you?" She asked, sounding surprised.
Trish looked at her "savior" for a moment, then smirked. "Cool it, little girl. I'm Trish. Nice to meet you." She said.
"I'm Rachel..." The girl said, then stopped, looking at Trish. "You have the same type of aura as a fiend." She said, slightly darkening her expression.
"Well, you aren't much better, no offense. But I'm a hellspawn. I was created to kill my partner, Dante, but he's a little more charming than I thought, so I decided to join him hunt down the demons." Trish said.
"My blood is cursed. I'm susceptible to becoming a fiend like the thing I just killed, but I'm stronger than any one of them I go up against. I'm even stronger than Ryu." Rachel said, looking down at her weapon dramatically.
"Well then, what do you say we have a little match? See who's the better demon or fiend hunter?" Trish said, starting to circle Rachel.
"Sounds fun." Rachel said, also circling.
Trish looked her opponent up and down, then smirked. "You must be getting the mother of all wedgies in that outfit. It looks like something you'd see a girl wearing in a strip club, or if she loves S&M." She taunted, getting a grin and drawing her pistols.
"I can think of worse outfits." Rachel said, thinking of Ivy Valentine's Soul Calibur 4 outfit. "But are we gonna talk about fashion or are we gonna fight?!" She shouted, swinging the hammer down to smash Trish, who narrowly evaded.
Trish fired at Rachel, who blocked a few shots, then spun in a small circle and shot her Petula's tail (basically some kind of weird grappling hook/whip) out and knocked the pistols out of Trish's hands before pulling out her own firearm, the Type 666 Heavy Machine Gun, shooting at Trish non-stop, catching her with some bullets in the calf of her right leg and actually hurting her, due to the bullets being highly-effective against fiends (and therefore demons and Hellspawns like Trish, which are the same thing), before Trish pulled out the Sparda sword and got into a crouching position, blocking the bullets. Rachel rushed in and jumped into the air, coming crashing down with hammer, forcing Trish down. Trish was strong, but she was indeed having a hard time forcing against the massive war hammer and the strength of the woman behind it. Rachel lifted up, but then spun the hammer around and threw a horizontal swing, smashing it into Trish, sending her flying into a wall.
"That's enough of this! Trish said, firing lightning out of her hand towards Rachel, who once again, either side-spun (she's not very agile, spinning one way or the other is basically her dodge) or blocked.
Rachel used one of her sorcery attacks, the Blades of Ouroboros, charging up energy while becoming invulnerable to Trish's attacks, firing blades of light (somehow made from fire and lightning) at Trish, cutting her deeply. Of course, with her regeneration, this wasn't much of a problem for Trish, but it did damage her. She got up and shot more lightning at Rachel, but by spinning around the hammer and spinning, she was able to dodge and deflect the lightning and getting close enough to used her more powerful, yet more ranged, sorcery: The Magic of Raging Aphrodite, making demonic roses and thorns come out of the earth and tear at Trish. Once again, although this did much more damage than the previous one, as the magic was, as said before, demonic. Trish was definitely out of the fight, but she was still alive.
"Not bad, you've certainly got some moves." Trish said.
"Well, you weren't half bad yourself." Rachel said, helping her up.
"You should swing by Devil May Cry sometime, we could always use another person on the staff." Trish said, giving Rachel the address, picking up her guns and leaving.
Reasons for the outcome:
1: While Trish is powerful, she's never had any real test of strength like Dante or Ryu have and Rachel may be stronger than Ryu, as seen when she effortlessly kills fiends with one swing that Ryu otherwise would need slightly longer to kill, although, to be fair, at these points, he usually didn't have giant weapons like hers yet. But even after he gets those weapons, it still seems easier to kill them with Rachel than with Ryu. Plus, Rachel seemed to be evenly matched with Lady in a fist fight and fatigue easily, so we could argue her strength isn't up to par with Dante's, Ryu's or Rachel's.
2: While Trish CAN use the Sparda sword, she's usually seen to rely more on her guns and her lightning power than the sword itself and somewhere along the line she gave up the sword, actually more than once, possibly (In DMC4 and the anime). Rachel often faces enemies with similar powers or firearms, so she's no stranger to blocking bullets and even demonic attacks from a demon with God of the Underwold status.
3: Trish is durable, but not so much as Dante, as seen when one of Mundus' attacks potentially killed her, when they had no effect on Dante afterward. Rachel's magic is not soul-stealing, but it is immensely powerful and demonic, plus it is shown to work on many fiends, so it stands to reason it would work on Trish.
4:Rachel uses Petula's tail for many things and in the first game, it was her only ranged weapon, so it would make sense she could use it to knock away Trish's pistols.
5: Rachel's gun is inscribed with special symbols solely for the purpose of destroying fiends, plus her gun is more powerful than the type of machine gun mounted on tanks, so if Lady's smaller, less powerful guns NOT specifically designed to kill demons could do so and hurt Trish (she never shot Trish, but she made it a point not to get hit by the bullets, so we can assume that, unlike Dante, these bullets would hurt her) Rachel's gun could much more easily do so.
6: Rachel has blocked at dodged attacks from a demonic Greater Fiend who rules the Underworld, so Trish's lightning, which was unable to harm Abigail, would be something Rachel could handle.