Just in case we lose data for the Mega Man X games for the first Playstation, I've managed to make three checklists. One each for X4, X5, and X6. They're as described below:

X4 checklist:
Defeat Frost Walrus and collect the W-Tank.
Defeat Jet Stingray and collect the Heart Tank and the E-Tank.
Defeat Slash Beast and collect the Heart Tank.
Defeat Web Spider and collect the Armor Piece.
Fight Colonel.
Return to Frost Walrus' stage and collect the EX-Tank.
Defeat Split Mushroom and collect the Heart Tank.
Defeat Cyber Peacock and collect the Heart Tank, the E-Tank, and the Armor Piece.
Defeat Storm Owl and collect the Heart Tank and Armor Piece.
Defeat Magma Dragoon and collect the Heart Tank and the Armor Piece.
Return to Web Spider's stage and collect the Heart Tank.
Return to Frost Walrus' stage and collect the Heart Tank.

X5 checklist:
Defeat Grizzly Slash and collect the E-Tank and colect the Falcon Armor Piece.
Defeat Duff McWhalen.
Defeat Squid Adler and collect the Falcon Armor Piece.
Defeat Izzy Glow and collect the Falcon Armor Piece.
Defeat Dark Dizzy and collect the Gaea Armor Piece.
Defeat The Skiver and collect the Heart Tank and W-Tank.
Defeat Mattrex and collect the Heart Tank.
Defeat Axle the Red.
Return to Duff McWhalen's stage and collect the Heart Tank the Falcon Armor Piece.
Return to Dark Dizzy's stage and collect the Heart Tank and the E-Tank.
Return to The Skiver's stage and collect the Gaea Armor Piece.
Return to Mattrex's stage and collect the Gaea Armor Piece.
Return to Axle the Red's stage and collect the Heart Tank and the Gaea Armor Piece.
Return to Grizzly Slash's stage and collect the Heart Tank.
Return to Squid Adler's stage and collect the Heart Tank.
Return to Izzy Glow's stage and collect the Heart Tank and EX-Tank.

X6 checklist:
Defeat Commander Yammark and collect the Heart Tank and the Blade Armor Piece.
Defeat Ground Scaravich and collect the Heart Tank and the Blade Armor Piece.
Defeat Blaze Heatnix.
Defeat Blizzard Wolfang.
Defeat Rainy Turtloid and collect the Heart Tank.
Defeat Metal Shark Player and collect the Heart Tank.
Defeat Shield Sheldon and collect the Heart Tank, the W-Tank, and the Blade Armor Piece.
Defeat Infinity Mijinion and collect the Heart Tank and the Blade Armor Piece.
Return to Commander Yammark's stage and collect the E-Tank.
Return to Blaze Heatnix's stage and collect the Heart Tank and the Shadow Armor Piece.
Return to Blizzard Wolfang's stage and collect the Heart Tank, the EX-Tank, and the Shadow Armor Piece.
Return to Rainy Turtloid's stage and collect the Shadow Armor Piece.
Return to Metal Shark Player's stage and collect the Shadow Armor Piece.