The strategy that I have been using has 4 required pokemon to cover basically all cases.
1st pokemon is Spinda with the hidden ability contrary. Make sure it knows the move Skill Swap. Nothing else here matters tbh. I've heard that having Dig is quite good if the spinda survives more than 1 turn so that it digs underground, then attacks. This uses up an extra turn compared to just attacking and dying immediately after skill swapping. But I never need to stall for a timer ball, so this is not really necessary.
The goal of the Spinda is to get the Contrary ability onto the Alpha so that when it gets the wild might boosts from breaking out of pokeballs it's stats are lowered instead of raised. Note that after a while these stat changes will be reversed. This happens more often if the Alpha has it's own stat boosting moves like swords dance or dragon dance that makes it reach the -6 cap faster or if it keeps healing and breaking out of pokeballs. The next pokemon helps with this though.
The 2nd pokemon I use is Swoobat with the Klutz ability and the Assault Gear item. This pokemon just needs to know the move Trick to put the Assault Gear onto the Alpha. When the Alpha is holding the assault gear it is unable to use any status moves like dragon dance, swords dance, recover, roost, aqua ring etc.
The most annoying Alphas that take the longest to catch in my experience are the ones that heal themselves or that spam stat changing moves which ends up reverting the negative stat changes caused by Contrary.
By putting the Assault Gear on the Alpha we mitigate the chances that this happens.
A good second move for the Swoobat is super fang. If it survives 1 attack, then it can deal at least half the Alphas health in damage before dying. Note that Swoobat can also learn Reflect and light screen if you want to help the Soak Smeargle survive a hit.
The last 2 pokemon that I have are the actual catchers.
The first catcher is a Smeargle that knows soak. This allows for grass types to be put to sleep with the move spore, which both catchers will have. Other good moves for the Smeargle are false swipe/super fang, Substitute, and Spore. I generally put leftovers on this Smeargle to allow it to heal from substitute uses.
The last catcher is generally a Breloom with the ability Poison heal. Give it the item Toxic Orb. This will poison the Breloom, but since it has poison heal this ends up having a healing effect. This healing is more potent than with just leftovers. This allows for basically infinite substitute uses, only limited by PP.
The Breloom should have spore, substitute, and false swipe. The last move is flexible. I have drain punch on mine.
To recap how battles usually go:
Open with Spinda. Immediately use skill swap to put contrary on the enemy.
Attack with the Spinda until it dies (or try hypnotize to then swap into the Swoobat, but that is risky as the Alpha might wake up and kill the Swoobat before it can Trick the Assault Gear onto the Alpha)
When the Spinda dies swap into Swoobat. Use Trick immediately to put the Assault Gear on the Alpha to prevent it from using status moves. Super fang with the Swoobat until it dies.
If the enemy is a grass type or resists normal type attacks I send in the Smeargle to Soak the Alpha. Otherwise I send in the Breloom.
Soak the Alpha if required. The Smeargle might die immediately after this, in which case swap to the Breloom.
Then Spore the Alpha to put it to sleep.
Then use substitute.
If the Alpha wakes up and attacks and breaks the substitute, then repeat the spore and substitute again.
When the alpha stays asleep for more than 1 turn you get a chance to use false swipe or super fang.
Bring the Alpha down to 1hp through false swipes/super fangs while keeping it asleep and hiding behind substitutes.
When it is at 1hp and asleep and you have substitute up start throwing timer balls. Chances are that by this time 11 turns have passed, so the timer ball will be at max catch rate.
Catch the Alpha.
For safety I have 2 more catchers on my team, but I usually only need 1 or 2 if it's an Alpha that needs to be soaked.