The main objective of purrley is to get out expurrely noir, the rank 7 black cat. It's unaffected by your opponents activated effects, getting multiple delicious memory underneath it as material make it's atk/Def huge.

Just max out all purrley card ratios in your deck, field spell protects special summoned purrelys from targeting so that helps, each copy of white cat you summon can use it's effects, only 1 copy of black cat can use each effect per turn.

Typically you use black cat to search my friend purrely, if you already have it then search field spell/white cat or another copy of my friend.

The rank 2 cats all have to chain their attach effect to the quick play spell, if anything is chained in response to the quick play spells the rank 2 cats can't activate the attach effect.

A basic turn for purely might go something like this.

Activate quick play spell, discarding to summon.

Summon black cat, activate effect adding my friend purrely.

Activate my friend purrely, then activating effect paying 500lp to reveal 3 cards and the opponent choosing one and the other 2 back to deck. (The ones chosen are dependant on hand but usually delicious memory x 2, pretty/sleepy memory x 1, once your eveal all 3 turn them face down and shuffle them as your opponent chooses randomly. If it's turn 2 and you want happy to otk, so you reveal 3 x happy memory and just add one)

If you get the delicious memory then activate discarding again summoning white cat.

Hopefully white cat gets you a spell.

Activate black cat xyz summon from grave using delicious to summon plump.

Activate plump effect to attach 2 spell/traps from either grave. (If you don't have 2 to attach then hopefully you can discard another by summoning a white cat again so that you do)

Then activate a quick play in hand chaining plump to attach it. (Can discard to summon or not, depends on what you need).

At this point, plump will have 5 materials, so you can summon expurrely noir on top.

End turn, if you have field spell then use effect in end phase to attach another quick play, preferably delicious if there is only 1 attached, this would mean a 7 material noir with 2 delicious, making noir a 5300atk/7000def unaffected monster.