Here we are at Gym number 2! As you come in, you'll be stopped by the same guy at the entrance of the Pewter City Gym. This time, he won't let you in unless you show him a Pokémon that's at least Level 15. Surely, you must have one of those? If not, you'll probably want to return to Route 24 and 25 and catch some more wild Pokémon for experience.
Know Your Match-Ups: Water
As you can tell from the layout of this Gym, its specialty is Water-type Pokémon. Water-types are weak to Grass and Electric and strong against Fire, Ground and Rock. For most purposes, Grass-types are ideal since they also resist Water--something most Electric-types cannot do.
From the entrance, step forward onto the glossy platforms. Towards the left is a female swimmer who will swim down to you if you enter her line of vision. There's no way to get around her without a fight, so get your Water-busting Pokémon ready!
We're going to assume you've brought a Grass or Electric-type. Or if your partner is Eevee, it has Buzzy Buzz in its moveset. If so, go nuts. Ironically, this Goldeen doesn't have Water-types, but it does have the Flying-type Peck. It shouldn't do a lot of damage regardless.
From here, you have the choice of avoiding the next two trainers. If avoiding's your game, instead of going straight up along the middle path, you'll want to go around and up the side paths in a Z or 2 shape. Basically, you want the swimmers along the side to be outside of your view (and thus their view).
Another Water-type, so nothing too complicated. This one does have Ice Shard, which is an Ice-type move that always goes first (unless your Pokémon is faster and uses a similar move). But even if you're leading with a Grass-type, so long as its healthy, it should survive Shellder.
The final Gym trainer has a Seel that knows Aqua Jet. Like Ice Shard, this is a move that always goes first (with the same caveat). But this time, since it's a Water-type move, your opponent will gain STAB when using it. However, it's only 50% more damage, ao shouldn't be problematic.
Gym Leader Misty
Misty is a tricky opponent who shouldn't be underestimated, even at this early stage in the game. Psyduck isn't too bad, although it can use Confusion to hit Poison-types for super-effective damage. That's most of the Grass-types you can use.
But similar to Shellder's Ice Shard, Psyduck doesn't gain STAB and if trained well, your Grass/Poison-types should be able to outlast Psyduck. If in doubt though, lead with an Electric-type--well, just Pikachu unless you've traded.
Finally, Misty has a Starmie, which is the real terror. This evolved Starmie gains the Psychic-type and has a powerful Water-type STAB in Scald, which has a good chance of causing Burn. It can also use Psywave to hit for 9 to 28 HP worth of damage.
Against Starmie, Grass-types are highly recommended. Poison-types don't need to worry because, like Seismic Toss, Psywave cannot inflict super-effective damage. That said, if you used your Grass-type against Psyduck, you will need to be careful of their health.
If in doubt, your partner is a good choice, but they need to be wary of Scald. Pikachu can obviously deal some solid damage with Zippy Zap. Meanwhile even if Eevee doesn't one-shot Starmie with Buzzy Buzz, it will inflict paralysis, making the fight easier.
Should you manage to stand your ground against Misty's crashing waves, she'll concede her Cascade Badge, as well as TM29 Scald. Originally, she gave Bubble Beam, but this is so much better. In addition to dealing impressive damage, it has a good chance to Burn, greatly weakening physical attackers.