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. 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.
Purple circle (around a Pokémon): This Pokémon is scared and will run away from 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 (SPE) increase the player's movement speed.
The maroon squares are WarriorGallade's suggestions for where to chase the Pikachu to effect easier captures.
Level Strategy
This mission seems more fair than the past few. Rampardos or Luxray will chase you relentlessly, and without the speed powerup found along the way, avoiding them is nearly impossible. Note on type matchups: resisted/immune Poké Assists deal 0.5x damage, but super effective Assists only deal 1.5x, so a disadvantaged Assist with strong utility can still be used effectively.
First three chambers: A long diagonal pathway ends in a near-unavoidable Rampardos/Luxray capture. The next diagonal room has 4 speed powerups: keep in mind they don't stack, so you only need to get one. (There are 4 in the case where the player is doing a multiplayer challenge with 4 players.) Three Rampardos/Luxray will chase you, but with a speed powerup they will not catch up if you are able to avoid battling them when they first approach. A third diagonal room holds some time extensions. The final teleporter will take you to the Pikachu chamber.
Pikachu chamber: Capture 5 Pikachu. There are only 5 Pikachu in the stage, and they will all flee from you. They’re agile, making this one of the hardest chases, even with the speed powerup. Try to lure them to the maroon squares, moving clockwise around the map. The southeast corner works best: hug the wall on your left, and while Pikachu may look like it will veer away, you’ll almost certainly be forced into an encounter. Wait for post-capture invincibility to wear off before moving, or you can’t initiate battle and may have to chase another lap. Note that the Pikachu's starting locations differ slightly based on the pattern.
Final chamber: Dodge the Rampardos/Luxray at the entrance (you outspeed it) and go clockwise around the outer path, the only reliable way to avoid the four patrolling Skarmory. Even one forced Skarmory capture makes S-rank very difficult. Grab the 30-second time bonus and press the tile switch; note that the location of the switch varies based on pattern. If the switch is at the north end (Patterns 2 and 4), you can safely return anti-clockwise, although be aware that Skarmory hitboxes are deceptively large, which may require you to retreat clockwise. If the switch is at the northeast edge (Patterns 1 and 3), activate it and return to the west edge spot where the tile switch opens up. Take the powerups you want, watch for one last rogue Luxray/Rampardos, then enter the red teleporter.
Pattern Identification
The location of the switches in the final chamber, as well as some powerups and Pikachu locations, is dependent on the pattern.
The first Pokémon the player sees is Rampardos: Pattern 1 or 2.
The first Pokémon the player sees is Luxio: Pattern 3 or 4.
On a Rampardos pattern, the Pokémon around the time powerup in the third diagonal room is Baltoy: Pattern 1.
On a Rampardos pattern, the Pokémon around the time powerup in the third diagonal room is Pachirisu: Pattern 3.
On a Luxio pattern, the Pokémon around the time powerup in the third diagonal room is Natu: Pattern 2.
On a Luxio pattern, the Pokémon around the time powerup in the third diagonal room is Baltoy: Pattern 4.
Minibosses
Rampardos, like a boss Pokémon, get agitated at 60% HP. Its attacks are similar to Bastiodon's, but it uses Rock Slide for its (!) attack and Headbutt for its (!!) and (!!!) attacks.
Rock Slide (!): Drops rocks in random areas of the screen at approximately 0.4 second intervals. This drops about 8 rocks. Possible to loop around, but requires luck with rock placements.
Headbutt (!!): Launches a Headbutt in the direction it's facing.
Headbutt (!!!): Launches a Headbutt in the direction it's facing.
Luxray doesn’t agitate, but has annoying attacks similar to Ampharos'.
Sparks (!): Generates a lot of sparks immediately around it. It is difficult to loop around.
Thunderbolt (!!): Charges for 1 second, then lightning strikes random spots for ~2.5 seconds. It is possible to loop around, but requires good luck.
Electric orb (!!!): Luxray summons an electric orb that circles around it at a short range, moving with Luxray, and lingering for several seconds (allowing it to regenerate health uninterrupted). It is difficult to loop around.
Skarmory doesn’t agitate, but is a time-waster with annoying attacks.
Whirlwinds (!): Launches 5 whirlwinds in the direction it's facing that travel to the edge of the screen. This has a very short delay between the telegraph and the attack, meaning it's easy to take damage from this.
Whirlwinds (!!): Same as the above attack, but only 3 whirlwinds.
Tornado (!!!): Skarmory launches a single tornado that moves slowly in the direction it's facing. It increases in size the further it moves, and lingers for about 5 seconds.
Boss
Strong beam (!): Launches a strong beam in the direction it's facing. This has multiple variations; see below for details. 10 damage per hit. Impossible to loop around.
Shock wave (!!): Attacks with a shock wave in a circle around itself. This is used twice per telegraph, with a short delay between the first and second. When agitated, this attack may manifest as Metagross hopping around the stage. 6 damage per hit. Risky to loop around and impossible in the agitated version.
Psychic spheres (!!!): Launches a barrage of small spheres that travel in all directions to the edge of the screen. When agitated, this may be used without telegraphing and can be used simultaneously to the beam attack. 6 damage per hit. Probably impossible to loop around.
Strong beam (!!!!): A wide beam that sweeps the screen in all directions. Impossible to loop around.
Variations for the (!) beam attack:
3 beams
2 beams
1 beam that circles the field
1 beam that makes a quarter-circle
1 beam that makes a half-circle
1 beam
1 beam that circles the field quickly (may be agitation-only)
1 beam that makes a 1/3 circle (may be agitation-only)
4 beams in a cross shape (may be agitation-only)
4 beams in a cross shape that converge to two (may be agitation-only)
S-Rank Tips
One of the easier S-ranks, especially once you have Pikachu chasing down. You’ll lose time on circling Pikachu and extra Rampardos/Luxray captures. Expect a high B/low A first try, with an S possible by attempt 2 or 3, as time is generous. The Rampardos variant seems slightly easier, especially with Piplup, thanks to Piplup's type advantage.
Partner Choice
Piplup is great again: slowing Metagross lets you spam loops more easily, since it’s fast enough to make chaining difficult otherwise. Only hold off on deploying Piplup during the psychic sphere barrage. Otherwise, launch your assist right after a laser attack to see which type it is, and if it’s !!, place your assist a decent distance behind and let it work. This is also a fun mission to grind AP, with a good variety of slates.
Alternative partner options: Fire can work as a super-effective Assist, but you would rather use a long-range Assist such as Flareon over a short-range Assist such as Typhlosion. Lucario, despite its type advantage, may not be ideal here since it lingers a while after attacking. However, using it as Metagross uses a slow beam attack can do a lot of damage.
Slate Spotlights
Staraptor can be obtained here as a rare drop (2%) from Staravia. WarriorGallade thinks this mission is better for grinding for this particular Slate than the next mission, even though Staraptor itself appears in that mission and its own Slate is a 20%, because the next mission is difficult to replay. Metagross' Slate can be obtained here, but WarriorGallade suggests that Metagross' Assist isn't really worth the time or effort.