When you're not punishing her, or being attacked by her, jump back and forth with SHL at her.
Do not try to pillar Samus. Falco's instinctively attempt this, but you'll just up-b screw attacked constantly. Instead, laser around while she shields, and maybe approach with a grab or spaced nair on her shield, but do not get right on her.
If she throws you up, DI in front of her (get hit by nair rather than a sweet-spot bair)
If she fires a missile at you while you're standing still, don't shine it, she'll jump over and dair you. Instead, dash forward or backward before shining, if that's the move you want to go with.
Back-airs are your best aerial counter against Samus.
If you lose a stock and Samus is at a high percent, just intelligently spam CC dtilt for the kill.
Spam lasers at a recovering Samus, maybe grab the edge and try a back-air edge-guard, but most importantly, do not stand right next to the edge after samus has grabbed on, since she'll just jump up with an aerial. Instead, stand back, and spam SHL + ftilt.
Always punish a laggy Samus with a grab or something she can't crouch-cancel. If she misses an up-b or a grab, don't hit her with a weak attack, or she'll just CC-dsmash you. Instead, grab or smash her.
These are the first ideas that come to mind.