I'm sure every boss is able to be defeated if you have good enough stickers. The World 1, 2, 4 & 5 bosses can be defeated easily enough without Things, Hopslippers help a lot and Fire Flower stickers for the snowman boss. Gooper Blooper could be done by someone really good and good sticker usage, but it along with the final boss are probably would be the hardest to do without Things. Gooper Blooper because of the Poison affect thing and the Final Boss because he's pretty durable and heals a lot.
I beat every boss except for Bowser without using Thing Stickers. Frankly, I don't even know if it's humanly possible to beat Bowser without using Thing Stickers.
Tower Power Pokey is just a long endurance test without Thing Stickers. And I mean a loooooooong endurance test. If you don't have at least two to two and a half pages full of Hopslippers and Flashy Jumps and at least 3 or 4 mushrooms, don't even bother, he'll kill you quickly. If he crumples you, well...good luck! Definitely the hardest of the bunch; took me 30-35 minutes to beat him without the Thing Stickers.
You just need good timing to dodge Gooper Blooper's poison attack and a lot of Hopslippers/Slaphammers. Make sure to bring a ton of mushrooms and useless stickers to waste in case you get poisoned.
I did Megasparkle Goomba, Petey Piranha, and Mizzter Blizzard not using things. Bowser? Things are literally required on that! Tower Power Pokey is nearly impossible without the Bat, and I accidentally used my Sponge in Gooper Blooper's battle and found it was super effective!