Wherever you are, Fly to Undella Town (or walk there if you’re nearby). Make sure your Pokemon are healed, then head west from the Pokemon Center. You’ll find Hugh standing here. If you speak with him, he’ll give you HM06 - Dive . How awesome!
After he does, he’ll ask if you want to battle. Feel free to respond with 'Yes' and initiate a battle, or respond with 'No' and come back later. If you do battle him, his party is as follows:
If Snivy was your starter
If Tepig was your starter
If Oshawott was your starter
If you defeated Hugh here, you can also find him chillin’ with the Old Team Plasma folks back at Driftveil City . Again, he’s up for another battle–with higher Level Pokemon–if you speak to him.
After the battle’s over or otherwise, head west towards the Marine Tube, but continue past it and into the house nearby. Inside, you’ll be met by Cynthia. She immediately takes an interest in you and challenges you to a battle. Accept if you wish, but do know that her Pokemon are pretty dang strong , since she is a former Champion.
You can also battle her once a day, so long as you’re in Spring (she’s also there during Summer, but won’t battle you then).
Trainer Battle: Pokemon Trainer Cynthia
Geez, Cynthia is on a totally different level from Hugh from just before. Her first Pokemon, Spiritomb can wreck you if you’re careless. It will gladly use Double Team to boost its evasion to untouchable levels, Hypnosis to sleep your Pokemon and Dream Eater to do damage and heal HP.
To make matters worse, Spiritomb has no weaknesses due to its near-unique typing. You can opt to attack it quick before its evasion gets too high. Moves that can’t miss like Aerial Ace are useful, but will do little damage thanks to its high defences. Also don’t let it sleep your Pokemon or it’ll heal itself.
Milotic isn’t as bad, but still tough. It has Attract to immobilise male Pokemon, so female Pokemon are ideal. It can also use Rest to heal all HP and simultaneously boost its Defence with Marvel Scale. Use Type Match-ups if you can, but avoid using Grass-types due to Blizzard.
Togetic is annoying with Thunder Wave, plus Extreme Speed (goes first) and Air Slash (gets increased critical rate due to Serene Grace), both of which are STAB moves. It also has Aura Sphere in case you wanted to use Rock- or Steel-types. Electric-types are good here for resisting Air Slash.
Ouch at Lucario … He has a bunch of strong offensive moves to cause pain including Close Combat and Flash Cannon. Fire- or Ground-types will excel, but they must be fast, as Lucario is fast and hits hard. Inflicting a Burn would help loads; Water-types will do okay, provided they have Scald.
Glaceon isn’t actually that incredible, thankfully. For one it’s slow, so you’ve got plenty of time to get some good hits in. Secondly it has many weaknesses: Fire, Fighting, Rock and Steel. In particular, Steel-types are recommended to resist Glaceon’s massive Special Attack.
Finally, it just has to be Garchomp , the monster of all dragons. If you can, quickly OKHO it with Ice Beam or another powerful Ice-type move. You must be FAST though as Garchomp is fast and has moves to counter nearly every type. If you can take the damage, Water-types will do OK.
From here, you can head straight to the Abyssal Ruins with your fancy new HM or head towards Black City (Black 2) or White Forest (White 2) via Route 14 , south of Undella Town.