Notes:

• If you catch certain numbers of Pokémon species, you'll unlock additional levels not required for Any% - at 50, 80, 100, etc. The fewer you catch, the fewer levels you unlock, which means you won't have cutscenes for those. Try to catch the same Pokémon multiple times instead of a variety, if possible. If the point totals are low enough, it might be worth dropping a multiplier to keep your catches down.
• You get 10 points per letter typed, so if there's something you don't want to catch for the above reason but you think the extra points might be useful, type up until the last letter to get as many points as possible for it.
• If the screen stops scrolling, catching the Pokémon is going to be faster than letting it go.
• If a Pokémon is on screen but there's no name displaying, you can start typing its name if you know it. This includes mini-bosses (e.g. Gengar, Electivire), but NOT bosses (e.g. Serperior, Groudon).

Route:

Here's the route that I use for my Any% runs. I've marked the medals you need on each level with [G], [S], and [B] (for gold, silver, and bronze). You can afford to miss one medal on one of the earlier stages, but you would need to have a perfect Semi-Colon Cavern to get the gold there instead of the silver.

Alt Rocky Range: [G] Catch all. HOME: Back out ASAP. X Resort: [G] Catch all. Space Hiking: [G] Stop at 300K points. Z Islands - [S] Catch the first Pokémon when it stops at the halfway point, catch the five appearing on the bridge, then catch the next when it stops at the goal. S Garden: [B] Catch each at a quarter of the way, about each six lampposts. E Tall Forest: [B] One catch at the end, then catch Serperior (one set of leaves). R Crag: [B] Catch one, let rest go until end, catch last. F Path: [B] Need 1,000 points. Catch quickly until you get at least 900 points, then let all go until catching the last at the goal. G Mansion: [G] Catch all; key spawns after six Pokemon. Last Pokémon is always Gengar. H Peak (15 medals required): [B] Catch last when screen stops scrolling. On Groudon, type three sets of "7TYUGH", then Groudon's name. N Cliff: [B] Need 1,000 points. Type out all but last letter until reaching the coins. Get all the coins, then catch the last two (second at the gate). M Waters: [B] Need 1,000 points. Type all but the last letter for all but the last Pokémon. Destroy all waves that appear. K Wood: [B] Catch four quickly, then wait for last. DO NOT open the coins - getting any of them results in a cutscene at the end of the level. O Snowy Path: [B] Need 1,500 points. Get 1,300+ points, then wait for last at gate. L Dark Path: [B] Catch last when screen stops scrolling. On Zoroark, type the appearing Pokémon (three random) then Zoroark's name. Semi-Colon Cavern: [S] Catch ten. If you missed a medal earlier, you can get a gold here if you get 22 consecutive catches without a mistake. You'll only have time for about that many, so you'll pretty much need to be perfect. Bracket Park: [B] Need 3,000 points. Catch five/six. Until end, get the flowers and type until the last letter of any appearing Pokémon. Bracket Lake: [B] Catch seven. Try to not have duplicates. Apostrophe Power Station: [B] Research two Pokémon (ideally the same species), then research the last at the switch. At the switch, do the tapping and catch Electivire. Sunset Forward Slash Way: [B] Catch last when screen stops scrolling. On Cobalion, clear the three tests, then type Cobalion's name when it appears. Function Tower (30 MEDALS): [B] Need 1,000 points. Catch two, then type all letters but last for remaining Pokémon. Left Expanse: [B] Need 5,000 points. Get as few coins as possible. Paradise Above: [B] Catch last when screen stops scrolling. On Virizion, clear the leaves, which are always ;[' (semicolon, left bracket, single quote), then type Virizion's name. Dark Depths: [B] Research nine Pokémon as fast as possible. Don't type additional letters. If you're fast enough, the screen will fade out before you reach the goal, but if not, type the last name at the goal. Right Ruins: Catch last when screen stops scrolling. Fight Reshiram (L - Light Stone) and clear its challenges, then type its name.