Here is the full list of all 57 60 Seconds! trophies - there are 50 bronze, 4 silver, 2 gold and 1 platinum.
Collect all trophies
Survive 5 days in your fallout shelter.
Last 10 days in your fallout shelter.
Stay in your fallout shelter for 20 days.
Stay alive in your fallout shelter for 40 days.
Beat the fallout shelter survival record.
Collect 10 soup cans from your house.
Collect 10 water bottles from your house.
Break or use everything possible in your shelter.
Break or use something in your fallout shelter.
Turn your fallout shelter into a madhouse.
Scavenge each item at least once.
Complete the government endorsed fallout drill.
It's all over.
Get rescued by the military.
Show those mutant roaches who's in charge.
Die in your fallout shelter.
Find a new friend.
Rescue the whole family.
Ram 1337 obstacles in your house.
Trim Ted's beard the trendy way.
Get to the shelter before the bomb hits.
Mutant!!!
Survival is overrated. Stay to see the fireworks!
Listen to the voices from beyond.
Meet the local 'law-enforcement'.
Ram a toilet.
Win a game in every mode on Little Boy difficulty.
Win a game in every mode on Fat Man difficulty.
Win a game in every mode on Tsar Bomba difficulty.
Always say YES and win.
Perform 30 successful trades.
Show your evil self.
Rescue someone from the bandits.
Receive a gift.
Always say NO and win.
Give and get back.
Fully explore your shelter.
Defeat three bandit attacks in one game.
Defend yourself without a weapon.
Don't forget to stock your shelter.
Ally with other wastelanders.
In Apocalypse mode grab only what a real gamer needs.
Put on a stylish hat.
Complete the holiday challenge.
Complete one challenge.
Learn to serve and obey the new masters.
Look at me. I'm the captain, meow.
Reach for the stars.
Find your way into the VIP bunker.
There can only be one.
Find a new companion.
Live through the nuclear blast as Dolores.
Reconnect with old friends.
Make them dance.
Find Deedee's apartment.
If you play it, they will come.