This is pretty delicate topic to answer because usually shades prevail between characters in terms of intelect and adaptability.
Not to mention intelligence is such a broad term defined by so many traits. Such as communication, resourcefulness, skill in quickly learning things or resolving logical problems. Abstract thought, observation and many other things.
As we know not all people are good at everything so person being very skilled in some of this disciplines does not mean he will be successful in others as well. Some are more talented for memorizing things, others are good at finding solutions when you put them in dangerous situations. Some on other hand express intelligence through good planning and utilizing knowledge they gained before in artful way etc.
But if i had to sort main characters in pokemon anime from most to less ingenious male/female protagonist based on few rough, however very notable examples and characteristics through which main fictional characters in pokemon anime were displayed as stereotypical this classification may be this is how i would do it:
1.)Clemont. its no brainer how we are having real genius in main cast. Posessing great craft skills in coming up with all kind of inventions, being great in natural science disciplines like math and physics expressing quick learning abilities and talent in making something remarkable out of nothing. Granted inventions are prone to failure, but no great scientist becamed successful over night and on first try.
Its based on stereotype but what can you do, many things in this anime are based on them.
2.)Brock. is character who on other hand display most brain and with in applying knowledge and wisdom in several challenging, dangerous situations,.
As evidenced in approaching wild pokemon like Tyranitar or Shiftry, knowing how to gain their thrust (like Stantler, Nuzleaf, Sharpedo etc). Revealing highly observing qualities in spotting most tiny details Ash and others overlook such as differences between nurse Joy and Jenny, poison berries and fruits, sick pokemon etc.
Followed with coming up with solutions how to settle down conflicts or stop pokemon, villains from rampaging. As evidenced in developing plans for slowing down and stopping various TR mecha such as Arbok tank, in using his water pokemon to weaken terrain turning it in mud allowing for Claydol to get caught in pkeball or TR mecha in attempt of stealing Mudkip being stuck.
Coming with idea how to resolve issues with tomboyish girl trainer Ditto or in Luxrio episode for example coming up with conclusion how to fool thieves by moving old charm from vault or see through TR tricks of moving pointers at clock backwards to buy themselves time.
3.)Misty. showed surprisingly high deduction skills, capacity to resolve logic problems, develop plans and searched for solutions in resolving issues with natural disasters, pokemon or criminals. Being quick thinker.
This can be evidenced in coming up with plan how to escape from sunk st. Anne ship memorizing whole blue print, disguise herself in breaking in pokemon daycare center to look for evidence to free Ash and Brock from jail.
Resolving riddles asked by gym leader Blaine and other people they met on journey with ease.
Developing plan how to get Snorlax across the mountain preventing to desolate whole island out of food.
Plan in resolving issue between two professor Oak exposing imposter through quiz test. Etc, etc.
Using pretty creative and cunning tricks such as deliberately sending her Togepi in fight with Ash Pikachu for Totodile, knowing how Ash pokemon couldnt force himself attacking baby. Or commanding Luvdisc to use pressure of water gun to open hatch in cave, followed with using ice beam on water gun creating bridge through which they could escape from Butch and Cassidy.
She showed to be very smart and observant due to her suspicious and blunt nature. For example i recall she could spot tiniest details which sometime even passed unnoticed infront of Brock eyes seeing through Jessie, James and Meowth disguise clothes more than once. Such as in episode where Temaku proposed Brock to marry her noticing from distance how they are wearing fake hair and beard for ie.
Noticing how ghost girl Lakoko created by Ninetales Illusion has no reflection in mirror realkizing its apparition.
Deducting through logic reasoning who stole Ash Phanphy egg by investigating when was floor washed last time to ease up case in discovering perpetuator foot proints or noticing scratches from claws on doorknob.
Warning Ash not to fall for basket full of candy and fruits in middle of road knowing its trap set up by TR or someone spoiling JJM trio fun.
And so on radiating with lot of clever ideas and smart reasoning.
4.) Cilan. gets mention because of very wide knowledge. His avid detective skills in discovering clues and source behind mysteries (such as missing Audino or Subway bosses crisis). Applying his expertize in reading compatibility between trainers and pokemon through how strong bonds they have and what kind of feelings prevail between them helping to figure out problems.
One of memorable examples was when he pointed out to Iris reason behind Excadrill not listening to her for years feeling ashamed of loss, not wanting to go through this burden again.
5.) Max. showed high level of knowledge, utility and volition. Attributed by big curiosity and ability to notice suspicious things exposing fraud or criminal activities.
Some of those examples include figuring out how cheerleading had nothing to do with Jessie and James pokemon becoming more resistant and stronger with attachs, but aromatherapy used by Sheridan pokemon in deceiving institute about cheerleading in Cheer Pressure.
Noticing Cacturn Jessie used against May using same moveset and battle style characteristic for Harley exposing his tricks.
Find out secret doors by inspecting maze walls looking for more thin places discovering secret doors in trying to find lost Wishmur and many other instances where his intelect came to expression.
6.)Serena. has one similarity with Misty and that similarity sprouts from fact of showing to have takent in coming up with clever ideas providing resolutions to problems. Such as leaving trace full of maccarons to help Ash and co find her and Bonnie when kidnapped by TR. When suggesting how to locate hideout of smuggler Dolan through Clemont gadget.
Offering plan how to get leaf through Chespin vine Whip for Pangoro instead of climbing up the mountain which was Ash idea.
Often realizing who stole all food like it was case with Chespin or Pncham etc.
So on account of being innovcative with ideas Serena showed some impressive cleverness there drawing similarity with first pokegirl.
7.)Dawn, May, Iris, Bonnie, Tracey. All had their eureka moments being averagely intellectual but compared to others in terms of being observant, aware of things happening around them, speed in resolving problems or various clues,. Riddles and challenges they didnt impressed me or showed same level of skill like some other above mentioned examples did imo.
8.)Ash. Eh, as much as i like him while he is at his best when battling often thinking outside the box. Coming up with weird, but highly unexpected strategies being pretty smart and virtuosic there.
Outside of that hes not brightest kid in the world often embarassing his companions by lack of knowledge about public things, dense and clueless nature. Faling easily for TR schemes or other persons who tried taking advantage of him not having knowledge and logic understanding to see through such things. Or lacking sometime resourceful and creative resolution of problems and clues compared to abilities some of his traveling friends displayed.
But hes improving as he matures and i still like him with this forgetful and bewildered touch to personality adding to his appeal.
9.)Well its JJM trio. Jessie, James and even Meowth while most leery, sly and smart of them three generally fail in wisdom, learning on mistakes developing better ideas, perception and proper planning. With their greed, overconfidence and inability to often find common language resulting in failing hard in accomplishing any task they set infront of themselves.
Quickly giving themselves away. But that was more for purpose of playing comedy relief role than anything else in reality. Since in BW it was showed they can be more competent and aware of their flaws avoiding to go in fights they cannot win if plot demands it.