Evolving weapons happen by combining a max level weapon with any level of a specific secondary support item. Once you have both of those items you must then kill an Elite enemy and open the chest that it drops. The combinations for the Whip is the following:
Bloody Tear – Whip + Hollow Heart
The Whip is unlocked by default and the Hollow Heart is first unlocked by surviving 1 minute as any character.
Hollow Heart can be found as a stage item in Mad Forest and Moongolow (Recommended to get the Milky Way Map from Dairy Plant first to make it easier to find these stage items though). It is also put into your passive item rotation once you survive over a minute with any character.
If you're interested in seeing what the combo is for the other weapons they are listed below in the spoiler tag :)
*** Spoiler - click to reveal ***
Hellfire – Fire Wand + Spinach
Death Spiral – Axe + Candelabrador
Holy Wand – Magic Wand + Empty Tomb
Thousand Edge – Knife + Bracer
Heaven Sword – Cross + Clover
Unholy Vespers – King BIble + Spellbinder
Soul Eater – Garlic + Pummarola
La Borra – Santa Water+ Attractorb
NO FUTURE– Runetracer + Armor
Thunder Loop – Lightning Ring + Duplicator
Gorgeous Moon – Pentagram + Crown
Vicious Hunger – Gatti Amari + Stone Mask
Mannajja – Song of Mana + Skull O'Maniac
Valkyrie Turner – Shadow Pinion + Wings