Everybody knows the set, but this doesn't make it less dangerous. Amnesia boosts Slowbro's decent Special, being able to reach the maximum 999 after three Amnesia boosts, letting Slowbro 2HKO Chansey with its STAB Surf at +6. Amnesia, like all boosting moves, also has the great side effect of further reducing the speed of paralyzed enemies, allowing Slowbro to muscle through paralyzed would-be walls a lot more easily. When playing Slowbro, it's really useful to know some significant damage rolls or otherwise have a damage calculator handy. As said, Slowbro has a good chance of 2HKOing Chansey but must be at +6. The same can be said about Starmie, although a 999 Special STAB Surf is a guaranteed 2HKO. On the other hand, Starmie is much more of a problem for Slowbro due to having a much higher critical hit ratio. Beating Tauros is about using Amnesia once and then 2HKOing it with Surf, although a +4 Slowbro stands a good chance of OHKOing Tauros. Snorlax, however, requires Slowbro to use Amnesia twice to get the 2HKO; a +6 Surf almost never OHKOes Snorlax. Zapdos also requires two Amnesia boosts, while Jolteon, like Tauros, is 2HKOed by a +2 Surf. Gengar will fall to two +2 Surfs half of the time, so it's generally advised to only use Amnesia once. Exeggutor and Lapras are 3HKOed by a +6 Surf; boosting either twice or three times is the way to go. All these calculations have been made considering that the opposition is at full health, so they may vary depending on the health of the opponent as well as on the situation of the battle itself.
Having said that, using Thunder Wave first is almost always a good idea. Slowbro is tied with Snorlax as the slowest Pokemon in the game, so paralyzing Snorlax is also a good idea to guarantee Slowbro is faster than it or to fish for full paralysis. Against common Slowbro switch-ins, such as Starmie, Gengar, or Electric-types, Thunder Wave will have to be used as they switch in, so that you can get a boost before they are able to attack. However, it's generally advised to switch Slowbro back after paralyzing the switch-in to get the chance to move two consecutive times the next time they switch in. This way, you can maximize your chances of KOing said check before they are able to score a deadly critical hit Thunderbolt. Even if Starmie or Chansey paralyze Slowbro back in order to outspeed again, using Thunder Wave yourself first was the best move, because the chances of beating an unparalyzed Chansey and especially Starmie are slim, as they can just keep using Recover or Soft-Boiled until Slowbro gets fully paralyzed and they get a chance to use Thunderbolt. An unparalyzed Starmie can also attempt to PP stall Slowbro out of Surfs as well.
Rest is perfectly suited for Slowbro. During the setup, Slowbro generally takes some residual damage and gets paralyzed, but Rest can keep Slowbro healthy and free of status. After maximizing its Special, no special attack can get past Slowbro's Rest without a critical hit, and due to Slowbro's great Defense and lack of exploitable physical weaknesses, it's going to be hard to beat Slowbro from the physical side without Explosion. Tauros, for example, needs a critical hit Body Slam and Hyper Beam to 3HKO Slowbro, which is the only way it has to get past Rest; furthermore, if Tauros gets paralyzed, its chances of beating Slowbro become very small. Snorlax, meanwhile, will generally have to resort to Self-Destruct to take Slowbro down. Rhydon has the luxury of being able to 3HKO Slowbro with its powerful STAB Earthquake most of the time, but will have to switch into the predicted Rest and is OHKOed by even a +0 Surf. As said, Explosion makes a good way to eliminate Slowbro, but an Explosion might not even guarantee that a full health Slowbro goes down or gets revenge killed easily due to Slowbro's already mentioned great Defense. Exeggutor's Explosion, for instance, will only hit Slowbro for around 60%. Lowering Slowbro to around 80% or forcing it to Rest first is the safest way to ensure that one Explosion is enough to let a physical attacker, such as Tauros, Golem, Rhydon, or Persian, to revenge kill it safely.
Psychic is a STAB alternative to Surf, and trades 5 extra power for a 30% chance of scoring a Special fall. As far as type effectiveness is concerned, Psychic gains a neutral hit against Lapras and Cloyster and a super effective hit against Gengar and Victreebel, three of which are effective Slowbro checks, but loses the neutral hit against Alakazam as well as the ability to OHKO Golem and Rhydon at +0, needing two Amnesia boosts to OHKO them. Seismic Toss Alakazam, in particular, will have the opportunity to force you to Rest before Slowbro is able to get past it. Psychic's lower PP could also be a problem against users of recovery moves, especially considering that, without Surf, Alakazam will also require more time to take down. It could also be an issue if your opponent keeps using Recover or Soft-Boiled and gets lucky with full paralysis. Having 8 fewer PP could also be significant in an odd Slowbro war.
Reflect is a possible alternative to Thunder Wave, as it doesn't change the general concept of the set, but changes the way it works in some way and some of its counters. The first thing to notice is the loss of Thunder Wave, which will be problematic in several match-ups. Unless you can paralyze Starmie with another Pokemon, it will hard counter Slowbro. Other specially based Pokemon, such as Chansey, Lapras, Gengar, and Electric-types will also become more problematic if you can't paralyze them; they will have a higher chance of scoring a critical hit Thunderbolt, as they will move first and avoid possible full paralysis. Lastly, Victreebel and Venusaur will have nothing to worry about a Slowbro lacking Thunder Wave unless its attacking move is Psychic. Letting Victreebel in for free could get especially problematic if it's packing Wrap.
The reward of using Reflect comes from the physical side. It almost ensures that none of Snorlax, Golem, and Rhydon will have a chance to take Slowbro down due to their low critical hit rate. Tauros will have a lot of difficulties too, needing two critical hit Body Slams to beat Slowbro while it Rests. Reflect is also great for weakening Explosions, which is one of the most common and "safe" ways of getting rid of Slowbro; even Snorlax's Self-Destruct will only manage around 40% damage. Reflect makes double Explosions necessary to lower Slowbro to the point where it can be revenge killed, which, for the opponent, involves sacrificing at least two Pokemon.