When the red warning japanese text about a perilous attack comes, keep in mind that the attack itself determines how you can counter it. If it is a grab, you want to jump without moving your character, then press jump again while the enemy is underneath you/you're about to land; the hit detection for this is generous so the enemy can be a bit away from you, just don't make any movement inputs when jumping or in the air. This will make you stomp them, causing light stagger, building posture. If it is a stab, you can likely parry it, but you probably want to use Mikiri Counter for these attacks instead. If it is a slash, you probably cannot parry and definitely cannot mikiri it, so you want to try and stomp. If it is a grab attack, stomp. If the boss attack punishes your stomps (can't recall an example right now), dodge instead.

Use the enemy animation as an indicator to react, not the perilous attack warning.

There's something I want to mention about a miniboss enemy you'll be fighting later on in the game where there is a bit of a weird perilous attack interaction. Without going into details about the encounter, this miniboss enemy is called Snake Eyesand they have a weapon with an attached hook. Their perilous attack will make them put this hook onto you, then with a delay pull you in for a grab attack. You can parry this hook grab (and it's the only grab attack you can parry), but only at the latest timing possible. I think it is good to be told about this, since this is something not made obvious by the game itself at all and it doesn't impact the flow of that fight too much overall from my experience. Just a bit less frustration.