Text of this section & map image are taken from WarriorGallade's post on the subject, supplemented with information from the official Prima guide book, and condensed/reorganized slightly. Used with permission.
Map
This Mission contains four different patterns of wild Pokémon that can appear. Click a thumbnail below to view that pattern's map.
Legend:
Blue tile: The player's start point.
Red tile: Takes the player to the boss room, once the condition has been met.
Green tile: Teleports the player to another specific location on the map.
Yellow tile: Standing on this tile makes a bridge appear between separate platforms, or lowers a barrier on the walkway. Tiles that need multiple players are marked with red dots that indicate how many players are needed.
Orange circle (around a Pokémon): This Pokémon is angry and will chase the player on sight.
Brown circle (around a Pokémon): This Pokémon is angry and will launch projectiles toward the player on sight.
Icons like this (darker) give the player extra seconds, determined by the number.
Icons like this (lighter) restore the player's Styler by the specified number of energy.
Icons like this (POW) increase the player's Styler's power by 20%.
Icons like this (PART) increase the player's Partner Pokémon's Poké Assist power by 20%.
Icons like this (DEF) reduce the player's damage taken by 1 (to a minimum of 1).
Level Strategy
This is another huge map, and clearly not designed for solo play. WarriorGallade needed to be Level 47 with 100 Styler power and a maxed Piplup to clear it, and even then, only with a C rank. WarriorGallade also reports that being level 99 didn’t make it easier. The problem here is simply that the required amount of distance traveled to open the boss room simply eats too much time, regardless of how many Pokémon the player avoids or how quickly they capture Magnezone.
The goal is to capture 4 Starly. The first two on the player's path, but the last two are scattered across a spiral maze that forces heavy backtracking. Time is extremely tight, and running out of time is an automatic game over.
First room: A Manectric guards a defense powerup. Take it if you’re low level and keep running out of energy; skip it if you want a high rank or a more reliable clear.
Second room: Pachirisu (Pattern 4) or Natu (Pattern 2) is better to see here than Bronzor (Pattern 1). Go right and take the teleporter for the first Starly. Return, then go north to the switch at the far end. Skip the battery powerups here to save time. If a Pokémon sits on the switch, you can activate it without a capture by positioning yourself carefully. Pachirisu is the easiest to avoid, Natu seems to stay still, and Bronzor sways in place, probably forcing a capture. Saving even a few seconds matters.
Large hub room: Heading right gets you the second Starly. Going up leads to a pair of teleporters, and below the teleporters, the center path leads to the boss teleporter. The center path is guarded by a Staraptor/Skarmory on each side, firing twisters that only hit you on the central path and knock you away from the path; timing this is difficult and getting hit can waste time. Around the boss teleporter are an attack powerup and a partner powerup. When first trying to clear the mission, taking this small detour (since you will have to leave the path the way you came to get the two other Starly) is worth it for the extra power. If trying to achieve a better rank or grind Slates, skip the center path to save time. Regardless, take the right teleporter when ready.
Spiral maze room: Scattered Bronzong (Patterns 3 and 4; bad) or Claydol (Patterns 1 and 2; terrible) chase and attack on sight, with limited vision but narrow paths and fast movement making them hard to evade or outrun. Bronzong is slightly easier to deal with since it can't catch up to you after its initial burst of speed when approaching you. Even your best case (avoiding 3 of 5 Bronzong) won't be enough for an S-rank. Don’t grind AP here; the next mission has far easier AP targets. To move forward, you will have to stand on each switch you come across, then retreat to the teleporter that leads back to the hub room and take the other teleporter in that room, all the way until you are at the center of the spiral and have caught both Starly. This back-and-forth is what makes the mission so hard solo, as you’ll pass the Claydol/Bronzong repeatedly. A 4-player party could clear it at breakneck speed; even a 2-player party has a huge advantage here.
Third Starly: Upon entering the platform at the middle of the spiral, you will be able to catch your third Starly, which is agitated, next to a switch. Capture it, step on the switch, and take the teleporter, which will take you to a room with a Manectric or two Voltorb and two chests containing 60-sec powerups. Take the powerups and go through the new teleporter. It will take you to an area underneath the right Staraptor/Skarmory; step on the switch to open a path to the outer path of the hub, then take the left teleporter to enter the spiral again toward the fourth Starly.
Fourth Starly: Enter the platform at the middle of the spiral and capture the fourth Starly on the bottom. Take the teleporter to another room with a Manectric or two Voltorb and two more 60-sec powerups. Take these powerups and take the next teleporter to find yourself under the left Staraptor/Skarmory. Step on the switch to open the path to the outer path, then head down the center pathway to go to the boss.
Pattern Identification
The available Pokémon depend on the pattern. The difficulty of the mission is slightly dependent on the pattern, and some Pokémon only appear in certain patterns (for Slate grinding).
The first Pokémon the player sees in the second room is Bronzor: Pattern 1.
The first Pokémon the player sees in the second room is Natu: Pattern 2.
The first Pokémon the player sees in the second room is Baltoy: Pattern 3.
The first Pokémon the player sees in the second room is Pachirisu: Pattern 4.
Minibosses
Both Claydol and Bronzong can teleport across the field, often right after an attack. Their HP is similar. Neither of them agitate.
Claydol is designed to waste your time. Psychic orbs break loop chains if you don’t lift your stylus. Its teleporting during the lingering orbs limits close-range assists to attack downtime or (!) windows.
Orb barrage (!): Launches a barrage of psychic orbs in the area it's facing, coming to about a 3/4 circle around it. Impossible to loop around.
Psychic orbs (!!): Launches three psychic orbs from its center that orbit Claydol. Lasts about 3-4 seconds. Possible to loop around.
Psychic orbs (!!!): Similar to the (!!) attack, except they orbit the area from where Claydol attacked. Possible to loop around.
The lesser evil. It sways for a second or two after telegraphing its attacks, giving extra loop time, and its attacks don’t persist, so exploitable blind spots make any Assist useful, despite its Steel typing. Close-range assists like Typhlosion melt it. Still eats 10+ seconds per capture, so capturing all 5 would cost about a minute.
Iron ball (!): Launches an iron ball in the direction it's facing, which travels in a straight line. Possible to loop around.
Psychic orbs (6 waves) (!!): Launches 6 waves of 3 psychic orbs, staggered at about 0.33 seconds, in the direction it's facing. Impossible to loop around.
Psychic orbs (2 waves) (!!!): Launches 2 waves of 5 psychic orbs, staggered at about 0.5 seconds, in a wide area in the direction it's facing. Impossible to loop around.
Boss
Electrical discharge (!): Launches a discharge in directions around itself. When agitated, this can be used untelegraphed while moving. 12 damage per hit. Very difficult to loop around, and probably only at the start or end of the attack.
Thunder sphere (!!): Launches a sphere in an arc in the direction it's facing, which lands on the floor and lingers. 8 damage per hit. Possible to loop around.
Electric barrier (!!!): Summons two balls of electricity that hover around it. 6 damage per hit. Very difficult to loop around.
S-Rank Tips
It may not be possible to S-rank this while playing solo. At level 72, with no detours, and a lucky Magnezone (~35 seconds), WarriorGallade was about 40 seconds short. At level 99 with good routing and only 3 Bronzong captured, he was about 25 seconds short, which isn’t nearly close enough unless you can somehow avoid every Bronzong. Experimenting with Gliscor for type advantage didn’t help, since Magnezone can’t just be blitzed with Assists. If you are trying to collect all Slates, you may need to either accept missing this one or find a friend to play with. That said, if anyone does manage to pull off a lucky S-rank victory on this and get it recorded, let me know and I can feature the video and strategy here.
Partner Choice
Piplup is likely still the best choice due to the investment you've put in it and the difficulty of finding AP to max other Pokémon at this time. If you're interested in grinding Slates, Lucario is also a good option due to its high damage, Slow effect, and type matchup with Bronzong, and its Slow effect is also helpful against Magnezone. Magnezone being Electric-type means its only weakness is Ground-type Assists, and Bronzong is weak to Ground-types as well; of the available Ground-types, Gliscor is likely better because of its pause effect, but it is very difficult to use effectively: try to time its hit on Magnezone for when the electrical orbs fade and then go nuts on loops.