Slowbro
Type Tier
Water / Psychic OU
Statistics
Stat
HP
95
 393
Atk
75
 248
Def
110
 318
Spc
80
 258
Spe
30
 158
Name Moveset

Tobybro

 ~ Amnesia
~ Surf
~ Thunder Wave
~ Rest

This is one of the most famous sets in Pokémon—the Tobybro! Basically, it works like this: you Amnesia, then you sweep.

It is really quite difficult to do though. First you've got to get Slowbro out, which is hard. It is a good counter for non-Seismic Toss Alakazam—Jynx also works well, and Ground-types are okay, but you don't want to take much damage before you set up. Slowbro can also work in a pinch as a Tauros counter with its huge Defense and Thunder Wave, but usually if you do that, the damage you take and the paralysis you may suffer will prevent you from setting up later.

Therefore, if you want to sweep, you will probably want to spread as much paralysis before hand as possible because Slowbro is slow, and has common weaknesses—most notably Electric. That way you can probably get two Amnesias up before they can hit you. Slowbro can often be a good way of getting Starmie paralyzed, if your opponent is relying on Starmie to stop Slowbro. Also, you probably want to wait until their Exeggutor has gone too.

With Slowbro's poor Speed and need to set up, it isn't really good at switching in often, so often it doesn't do very well at stopping Tauros, really you don't want to switch Slowbro in against anything other than Jynx more than once ideally. Seismic Toss Jynx can be a pain as well.

Other Options

Reflect can work though it's not necessary since his Defense is already excellent. Blizzard is a good option to hit Grass-types post-Amnesia. Earthquake is OK but not recommended.

Opinion

Slowbro is a good Pokémon, but it is a bad luck magnet. If you are ever just about to finish off your opponent's last Pokémon with Surf when your opponent's Chansey gets a critical hit Thunderbolt, don't say I didn't warn you. It's hard to set up, and with many things packing Thunderbolt and critical hits being common on RBY (especially on Pokémon like Starmie), it only takes some luck to screw Slowbro up.

Counters

Razor Leaf will always critical hit and therefore penetrate its Amnesia. Therefore, Victreebel, and Venusaur make great counters as they resist Surf as well, though the odd Psychic Slowbro may hurt them. Zapdos hurts even when you have an Amnesia up and may CH in the long run, not to mention it has Light Screen sometimes. Thunder Wave makes Slowbro even slower than his Paralyzed opponents too. Raichu, Electrode, Electabuzz, and especially Jolteon can scout for Thunderbolt critical hits, but will be severely limited by being Thunder Waved.

Starmie's own Thunder Wave, resistance to Surf and Psychic and his Thunderbolt from 298 Special and a kickass critical hit rate will screw Slowbro over nearly every time. Lapras resists Surf as well, and while he doesn't have the awesome critical hit rate, he can still try with Thunderbolt, or slow down Slowbro with Body Slam paralysis and Confuse Ray. Light Screen Chansey can stall Slowbro out of Surfs, usually it will either run Thunder Wave or Thunderbolt as well, both of which can be a major hindrance. Even without Light Screen Chansey is not to be taken lightly. Snorlax with Thunderbolt and Amnesia goes for a long stall war, and Snorlax may always choose to blow himself up with SelfDestruct.