The Predator doesn't have any stealth skills to begin with, so there's no point sneaking up on anything.
If you use the Alien's harvest execution, you'll lose your facehugger ability for a while.
Make sure you pull off as many executions as possible to keep your health bar topped-up.
Both the Alien and Predator earn Xeno and Honor points independently of each other. Use these points in the Store to upgrade your character.
The Predator's heat vision allows you to spot trip lasers.
Rapidly press attack buttons to whittle away an opponent's health, to the point where a skull appears above its head. This means you can execute a fatality. Press the corresponding skull on the bottom right corner of the screen, then quickly follow the on-screen prompts to deliver the knockout blow. Doing this refills your character's health meter.
You'll cover more ground by performing a lunge. Simply tilt the virtual analog stick in the desired direction and press the B button. This is the best way to avoid taking damage from enemies carrying ranged weapons.
Don't forget to block, which you can do by pressing the B button while standing still.