to pull it off you're gonna need the following:
- alakazam (i saw you already have one. it's the bulkiest 'mon at level 1 and teleport is flat out amazing, so yeah)
- 3 frustration tms (2 of them are obligatory. the other one is optional, but 2 of the 3 floors that spawn chansey have azumarill, a pokemon with over 90 hp that can threaten alakazam even through its stellar bulk, so keep this in mind)
- link box
- escape orb (self-explanatory)
- friend bow (^)
- cleanse orb or a non-stick cap (unless you wanna end up like me)
- mobile scarf (you get this after doing the gengar sidequest, but you can also buy one from kecleon in level 1 dungeons iirc)
- as many food supplies as possible (super duper important, as well as a max elixir or two)

optional: reviver seeds, but you shouldn't need those if you tread carefully), x-ray specs (probably my most used item in the whole game, but it is not obligatory by any means)

as far as procedures go, just get to the first floor where chanseys spawn (very easy with alakazam's natural bulk, teleport and frustration to nuke anything you can't run away from). i don't recommend recruiting any other pokemon along the way, as it could possibly be bothersome while waiting on a chansey spawn, but you do you. after that, explore the whole floor with your no-stick-cap on (to guarantee you don't stumble upon any undesired sticky trap or any other sort of unexpected shortcoming) and then equip alakazam with the mobile scarf. stay there, defeat some enemy pokemon in the meantime so the floor doesn't get clogged up and RUN TO A WALL EVERYTIME YOU SEE AN AZUMARILL (it bubblebeams for afar for around 50 damage, so do not ever think about messing around with them). try to defeat the azumarills by maneuvering around the wall or simply ignore them (can bite you in the ass later on, but it's better than running into your guaranteed death!). keep doing this until chansey shows up and hope you get lucky. if you don't, just rinse and repeat on the next two floors with chansey spawns. for what it's worth, floor 77 is probably the most bearable one as far as enemy pokemon go, but you want to maximize your chances of finding Chansey by trying your luck on every single floor, so yeah. have fun!