There are many trophies from past nintendo games you can collect. Alot of them can be found on 1-player modes and lottery.But some of the 300 trophies are special and can only be obtained by completeing certain tasks.
GOOMBA: Beat Trophey Tussle 1 in event mode
ENTEI: Beat Trophey Tussle 2 in event mode
MAJORA's MASK: Beat Trophey Tussle 3 in event mode
LON LON MILK: Beat Target Test with all 26 characters.Must be less than 1500 seconds
CAPTAIN OLIMAR: Have a "Pikmin" game file saved on your memory card
FINAL DESTINATION: Get the Final Destination stage
BATTLEFIELD: Get the Battlefield stage CELEBI: See Celebi in a pokeball
DONKEY KONG JR.: Beat classic mode with ALL main characters
F-ZERO RACERS: Beat adventure mode with ALL main characters
MEOWTH: Beat all star mode with ALL main characters
WARIO: Beat all star mode once
MR. RESETTI: KO 5 enemies on cruel melee
MASTER HAND: Beat classic mode on hard without using a continue
CRAZY HAND:Beat classic mode under 9 min.
GIGABOWSER:Beat Gigabowser on Adventure Mode
UFO:Play vs. mode over 100 times
KRAID: Play vs. mode 50 times
FALCON FLYER: Play vs. mode 150 times
GAME AND WATCH: Unlock Flat Zone
SANDBAG: In homerun contest hit sandbag over 1300 feet
PAPER MARIO: In homerun contest hit sandbag over 1600 feet
TARGET: Complete target test with all main characters
SHERRIF: Complete target test with a total time less than 700 seconds
MEW: Complete ALL star mode on hard without using a continue
LANDMASTERTANK: Get 1000 KOs
SAMUS'S STARSHIP: Escape Brinstar
CELEBI: Get all bonuses
WIREMAN(MALE): Beat 100 man melee under 3 minutes
WIREMAN(FEMALE): KO 100 enemies on multiman melee
FIGHTING WIREMEN: Beat 15 minute melee
TRAINING MODE TROPHEYS
METAL BOX: 11 combos
LIPS STICK: 21 combos
BUNNY HOOD: 121 combos