For this Warframe Riven Challenge I recommend using a strong tank Warframe like  Rhino/Rhino Prime  or Inaros - this will allow you to ignore mobs during the boss fight and focus your melee attacks on the boss in order to build up and keep the melee combo counter. See the linked articles for Rhino and Inaros tank builds.

Next, equip a Venka or Venka Prime and use a build similar to the one below.

Important: Make sure to equip the veiled Riven and any other required items, e.g. a pet, Dragon Key etc.

Go to Mars and start the War mission in solo game mode. When the capture target Lt Lech Kril is in his invulnerbility phase, just keep slashing him with your melee weapon to build up the combo multiplier and keep it above 6x for at least 30 secs.

Your melee combo counter is displayed in the lower right corner - in the image above it is 3.25X

First time I did this challenge I had to sustain a 3x combo multiplier with an Extinguished Dragon Key equipped - I actually completed the challenge just by killing mobs with my Venka Prime on the way to the boss. Very easy challenge with this setup. After the changes to melee damage this Riven Challenge now require you to sustain a 6x combo multiplier.