PSA: Back just before the victory of your team and buy all three items.
Resilience - Building a Better You [Active only in matchmade PVP modes while wearing a Worlds icon]
- Win a game where you bought Infinity Edge -AND-
- Win a game where you bought Morrellonomicon -AND-
- Win a game where you bought Randuin’s Omen
I know riot's intention behind this mission was probably to encourage players to play multiple games with different champs; mainly ones who favor one of the three listed items.
& a lot of people are complaining that teammates are trying to build all all three during a single match which results in more deaths.
But you just need to have them in your inventory when you win the game.
So play the game like normal, get right up to their nexus swarming the shit out of them & back, sell everything and buy all three items.