Evolutions are when you combine a weapon and a passive item to get a stronger weapon. Unions are when you combine 2 weapons to get a stronger weapon. You need to get the desired weapon/weapons to level 8 then open any chest and you'll get the evolution or union. There are about 24 different evolutions and unions. Here's how to get them.
Evolutions:
Whip+Hollow Heart= Bloody Tear
Magic Wand+Empty Tome= Holy Wand
Knife+Bracer= Thousand Edge
Axe+Candelabrador= Death Spiral
Cross+Clover= Heaven Sword
King Bible+Spellbinder= Unholy Vespers
Fire Wand+Spinach= Hellfire
Garlic+Pummarola= Soul Eater
Santa Water+Attractorb= La Borra
Runetracer+Armor= NO FUTURE
Lightning Ring+Duplicator= Thunder Loop
Pentagram+Crown= Gorgeous Moon
Gatti Amari+Stone Mask= Vicious Hunger
Song of Mana+Skull O'Maniac= Mannajja
Shadow Pinion+Wings= Valkyrie Turner
Flames of Misspell+Torrona's Box(Max level) = Ashes of Muspell
Glass Fandango+Wings(Max Level) = Celestial Voulge
Clock Lance+ Silver Ring and Gold Ring(Both max level) = Infinite Corridor
Laurel+Metaglio right and Metaglio left(Both max level) = Crimson Shroud
Bracelet= Bi-Bracelet
Bi-Bracelet= Tri-Bracelet
Unions:
Phiera Der Tuphello+Eight the Sparrow+Tiragisu= Phieraggi
Peachone+Ebony Wings= Vandalier
Vento Sacro+Bloody Tear=Fuwalafuwaloo
For the max level evos and unions you just need to max the passive item instead of only the weapon.
Note: apparently you don't need the Glass Fandango and Flames of Misspell evolutions for this achievement, but do them just in case.
Let me know if I missed something.