Heh, don't laugh at me for this, my first run though of Silver, I've never had Gold, I had probably the most trouble with Jazmine. I got through everything else with relative ease, bar Ice Path, but we'll get to that in a minute. See, here was my thought process at the time, Steel is a metal, Water is... well, water, what happens to metal when it's exposed to water over time? Rust! Thus, Water must be effective against Steel, right? I remember I had Poliwhirl (since I had no one to trade with for a Politoad *forever alone*), Gyarados (not Red Gyarados) and Quagsire. Back then I never knew the epicness of a Quagsire and called it a reject, but that's not even on topic.
So yeah, her Magnimite took me down Quagsire and Quagsire was taken out by her Steelix. Eventually I took her down, with the Water types, I might like to add. And I remember seeing her in the show with her Steelix before I even got Silver and I was like, HUERGVKAFDEGWEFVEQFGHADS!!!11!!!1111!1!!!!1!!! I WANIT! But again, off topic. And of course the personal hell that was Ice Path, I could not, for the life of me, get passed that first puzzle. By the time I had gotten passed it, I had gone back and caught everything I could (including Delibird, which wiped out my stock of Ultra Balls, I ended up using a Great Ball on it and got it) thinking that maybe if I did, I'd be shown the way.
Lol, those were a couple of troubles I had.