Single Player
Simple (Classic)
Easy - Sticker [Running Chibi Robo]
Normal - CD [Icicle Mountain (DX)]
Hard - CD [Staffrole (Smash Bros.)]
Very Hard - Figure [Mario (Strikers)]
Intense - Figure [Crazy Hand]
Simple with 20 or more characters - Figure [Master Hand]
Simple with all characters - Figure [Mario (Paper)]
SSE (Story Mode)
Have "Ike" join your party - CD [Ike's Theme]
Have "Captain Falcon" join your party - Masterpieces [F-zero]
Have "Ness" join your party - Figure [Franklin Badge]
Complete the SSE - Figure [Ancient Minister]
All-Star
Easy - CD [??????]
Normal - Sticker [Perimi (Animal Forest)]
Hard - Figure [Kathryn?]
Very Hard - Figure [Dynablade]
Intense - Figure [Mewtwo]
Complete All-star without using a continue - Figure [Pichu]
All-star with 10 or more characters - Figure ????
All-star with all characters - Figure ?????????
Event Match
#3 - Figure [Halberd]
#4 - Figure [Paltena]
#8 - CD [????????????/?????]
#13 - CD [Legendary Air Ride Machine]
#14 - Figure [Red Pikmin]
#15 - CD [DeDeDe's Theme]
#18 on Hard - CD [?????]
#19 - Stage [Mario Brothers]
#24 - CD [Fire Field]
#25 - Stage [Spear Pillar]
#28 - Stage [Electro Plankton]
#33 on Hard - CD [???/??]
#37 - CD [???]
#38 on Hard - CD [Star Wolf (Star Fox Assault)]
Arena
Target Test
Lv1 - Figure [Apple]
Lv1 with 10+ characters - Figure [Stafy]
Lv1 with all characters - Figure [Super Scope]
Lv1 within 15:00 - Figure [Paltena's Bow]
Lv2 - Figure [Peanut Popgun]
Lv2 with 10+ characters - Figure [Pellet]
Lv2 with all characters - Figure [Explosive Crate]
Lv2 within 19:00 - CD [Excite Truck]
Lv3 - Figure [Wario Bike]
Lv3 with 10+ characters - Figure [Ashnard]
Lv3 with all characters - Figure [Silver]
Lv3 within 20:00 - Figure [Ray MkII]
Lv4 - Figure [Barrel Jet]
Lv4 with 10+ characters - Figure ??????????
Lv4 with all characters - ??????? ?
Lv4 within 32:00 - Figure [Cardboard Box]
Lv5 - CD [Title (3D Hot ralley)]
Lv5 with 10+ characters - Figure [Casual Clothes Link]
Lv5 with all characters - Figure [Cyborg Ninja]
Lv5 within 30:00 - Figure ??????
Homerun Contest
Play with every character - Figure [Sand bag]
single character 300m - Sticker [Boo (Mario Tennis 64)]
Single character 400m - CD [Clu Clu Land]
Single character 500m - Figure [Home run bat]
5000m Total - Figure [Bumper]
8000m Total - Figure [Banana Being?]
10000m Total - Figure [Shy Guy]
12500m Total - CD [???? ?????CM?????]
15000m Total - Figure [Golden Hammer]
Multi-man Brawl
100-man Brawl - Figure [Pitfall seed]
100-man Brawl with every character - Figure [Zako Blue] (use a golden hammer?)
100-man Brawl within 4 minutes - CD [100-man melee (DX)]
100-man Brawl within 3-1/2 minutes - Sticker [?????]
Survive 15-minute Brawl - Figure [Zako Green]
50 K.O.s in Endless - CD [Mach Rider]
100 K.O.s in Endless - Figure [Zako Yellow]
5 K.O.s in Cruel Brawl - Figure [Zako Red]
10 K.O.s in Cruel Brawl - Sticker [?????????]
Boss Rush mode (cannot use golden hammers as far as I've heard)
Easy - Figure [?????]
Normal - Figure [??]
Hard - Figure [Dark Cannon]
Very Hard - Figure [??????]
Intense - Figure [??????????]
Boss Rush with 10+ characters - Figure [?????]
Boss Rush with 20+ characters - Figure [?????]
Boss Rush with all characters - Figure [???????]
Training
10+ combo - Figure [Banana peel]
400 combos total - Figure [???]
...the rest to come in a little bit. I didn't bother translating some of the reward names, as you probably noticed