
Lichdragon Fortissax; Patches; Draconic Tree Sentinel; Margit, the Fell Omen; Alecto, Black Knife Ringleader and Glintstone Dragon Adula
And did you know them all?
Clarifying some technicalities:
This is all in one Game Cycle. If you go into New Game immediately with the minimum number of Boss fights, 11 btw, you can technically lock yourself out of 154 (or 196 with the DLC) Boss fights, because you cannot go back to the Game Cycle you just beat and left, but also technically you could defeat whatever you want in the NG+ game cycle. So you can never truly lock yourself out… But as I said, this is all for one Game Cycle without going to NG+. (Also no glitches or cheats.)
How you can lock yourself out of them:
Fortissax
If you kill Fia at the very end of her quest, in the Deeproot Depths after defeating her Champions, you have permanently locked yourself out of fighting this dragon. If Fia is dead, you can't enter her dream to fight the dragon, and there's no way to revive her. This is also the only point where you can brick the quests; the quest design is very robust; belief me I've tried to sabotage it numerous times.
This is probably the most well-known one, since, if you choose the jerk answer to her question, she literally says "I see. Then you must kill me. […]".
Patches
Defeat Rykard without ever interacting with him. He will be completely gone from the game, and his equipment and Bell-Bearing are in the Murkwater Cave.
Draconic Tree Sentinel
Defeat Maliketh and turn Leyndell into the Ashen Capital, and he will be completely gone. For this to happen, you need to access the Capital from the underground by defeating: Radahn -> Gargoyles -> Fia's Champions.
Margit, the Fell Omen
Defeat Morgott. If Morgott is defeated, then no more Margit; you can waltz right into Stormveil Castle unmolested. btw Morgott drops the Talisman Pouch if you haven't defeated Margit before him.
Okay, I'm only 98% sure you can lock yourself out of these Boss fights. I personally locked myself out of the four fights above but haven't personally tested these two.
Alecto, Black Knife Ringleader and Glintstone Dragon Adula
You need to brick Ranni's quest, which is quite hard to do, since the quest is so forgiving. First collect and waste all 10 Celestial Dew items in the Church of Vows. Then make Ranni mad so that she disappears from the game. You can do this by killing Blaidd early or completing Seluvis' quest. With her gone and no way to get her back, you cannot get the Dark Moon Ring, and so you can never access Moonlight Altar, where these two Bosses reside.
I hope you enjoyed my rambling about something pretty niche in Elden Ring (ᵔ◡ᵔ)
Also, if you have questions or you know something that I don't, feel free to comment.
Edit: Okay, above are all the Bosses you can lock yourself out of in the base game, but you can also lock yourself out of a singular boss fight in the DLC:

If you kill Dryleaf Dane in Enir-Ilim, you can't fight him at the Moorth Ruins anymore. Yes, the fight at the Moorth Ruins has a Boss health bar for some reason. It totally slipped my mind.
I'm also unsure what exactly the point of no return for his quest is. I never tested the failure condition of his quest in detail. Killing him in Enir-Ilim definitely locks you out, but, despite what many online sources say, I don't think burning the sealing tree locks you out.
Those are some interesting recommendations!
I don't think I've heard of any of them before (maybe some screenshots from Still Wakes the Deep?).
Is the fighting gameplay in the The Sinking City any good or is this more about the world?
When I finally want to play something other than Soulslikes again, I will definitely look at these games.