Here is the full list of all 49 Heart&Slash trophies - there are 34 bronze, 12 silver, 2 gold and 1 platinum.
UNLOCK ALL CHARACTERS, EQUIPMENT AND UPGRADES
BEAT QUASSY WITH A FULLY UPGRADED RUBBER DUCK
BEAT QUASSY WITH THE PROTOTYPE
DEFEAT TWENTY OF EACH DOG'S PARTS
TOGETHER WE RISE
SIDE WITH SLASH IN THE FIGHT AGAINST QUASSY
FINISH A LEVEL UNSCATHED
DEFEAT FIFTY SMALLBOTS WITH A FIRE BACKPACK
DEFEAT FIFTY SMALLBOTS WITH A FREEZER BACKPACK
DISPLAY YOUR COMMITMENT
DEFEAT FIFTY WORMS
DEFEAT YOUR FIRST C.O.P.S. FLASHBANG
UNLOCK ALL BLADES
FIND SLASH IN THE OUTSIDE WORLD
UNLOCK ALL FIST BASED WEAPONS
HELP SLASH EXIT THE FACTORY
USE YOUR HEAD AND SAVE SLASH
DEFEAT FIFTY LASER ARMED ENEMIES
DISRESPECT THE AUTHORITY
DEFEAT TWENTY FIVE SMALLBOTS IN THE CITY
DEFEAT TWENTY FIVE TRIPODS
CLEAN THE REMNANTS.
SURVIVE SLASH'S CHALLENGE
BEAT THE UNBEATABLE
SURVIVE FIFTY ARENAS
SURVIVE THE DOCTOR'S CHALLENGE
DEFEAT FIFTY SMALLBOTS WITH A BACKPACK
DEFEAT FIFTY ARMOURED ENEMIES
DEFEAT ONE OF EACH ENEMY CARRYING A BLADE OR A SAW
DON'T BE MEAN
BEAT QUASSY AND UNCOVER THE TRUTH
EQUIP YOURSELF COMPLETELY
LONG LIVE THE QUEEN
DEFEAT TWENTY FIVE ENEMIES WITH A BACKSTAB
UNLOCK ALL AXES
DEFEAT ONE HUNDRED SCAVENGERS
BAT FIFTY MISSILES
REACH FIFTEEN HEARTS OF MAX HEALTH
DEFEAT FIFTY C.O.P.S. ENEMIES
DEFEAT FIFTY ELITE ENEMIES
DEFEAT ONE HUNDRED SMALLBOTS
HAVE YOUR ENEMIES DEFEAT TWENTY OF THEIR OWN
DEFEAT ONE HUNDRED NIMBLEBOTS
DEFEAT ONE HUNDRED BIGGRUNTS
DEFEAT FIFTY SHIELDED ENEMIES
DEFEAT ONE HUNDRED FLYBOTS
DEFEAT YOUR FIRST MAGNET
DEFEAT THE GUARDIAN
UPGRADE A WEAPON AND LET THE GOOD DOCTOR KNOW