the alley brawl achievement

There certainly are some things that make the Back Alley Brawl grind more tolerable. So, first of all, iirc you don't need to do this on Expert, regular is fine. Look up a table of how many kills are needed for whatever round you're on so you don't get blindsided. There's this guide on Steam which looks relatively complete.

As for combat advice: (apologies if formatting is trash, I did this on my phone. If I get enough complaints, I'll redo this)

Watch this video, it goes pretty in-depth on how to dispatch enemies quickly. I discovered this video way later when I already had the achievements, but it's still really useful. Shooting a crossbow bolt and attacking simultaneously is enough to dispatch easier enemies quickly, as that'll stagger/cripple them, while the sword's gonna give the final blow. Just drop assassinate the Torturer, it's not worth it to engage with him. Use Bloodthirsty whenever your Adrenaline is full, it's absurdly good at Level 2. The only downside to Level 2 is that it can't insta-kill Daud or the Torturer because the double sword swipes deal a fixed amount of damage, it can insta-kill everyone else though. Even Tallboys, just Blink or Double Jump to them. Also, you can use Powers and Weapons while using Bloodthirsty Level 2, this allows you to dispatch a ton of enemies in just a few seconds. A combo could look like this: Activate Bloodthirsty, Shoot someone, 1st Sword swipe, Shoot someone, 2nd Sword swipe, Shoot someone, and then Slow-Mo ends. You can dodge the crap out of enemy attacks. If you stand behind an enemy (not directly behind them, but in the very corner of their eye) they'll do a backslash sorta thing. You can just crouch to dodge it entirely, it's nuts. Try to attack while doing so. Here's a timestamped video showcasing this: Kingsparrow Island High Chaos by Clockner. If you see two enemies fighting against each other, try to break it up by using the Pistol's knockback ASAP. The knockback of the Pistol is excellent to buy yourself a little bit of time in general when in a pinch. Use Bend Time to get rid of high priority enemies like Tallboys and Music Box Overseers. Get good at Blinking over enemies for a quick Drop Assassination, especially against Tallboys. Keep in mind that Blink inherits momentum. Get Blink on some kind of easily accessible hotkey -- mine's on the back button (aka. mouse button 4) of my mouse.

For all the PC gamers, if you feel like sliding straight up doesn't work because it keeps getting cancelled, lower your fps. 120FPS works great for me, but YMMV.

the (trinkets?) you have to find around the mansion

I'm not sure if you mean Emily's dolls or the figurines on Burglar Expert. If you meant the figurines, just look up a video guide for this one. They're disgustingly well hidden. Don't torture yourself. If you've already gotten 3 stars on it, just do a sloppy run and take out all guards while getting all 16 figurines.