I always thought the Black Knight from Fire Emblem Path of Radiance and Radiant Dawn would have been an excellent choice.
Once summonded, he slowly walks a few steps and then swings his Alondite in the same way he attacks normally in the games. Then he shoots a long range shockwave attack or two, does a Critical attack and an Eclipse attack (he swings his sword a few times for both of these), and then shoots a long range Critical shockwave attack. Of course, he wouldn't have to do all those, nor necessarily in that order.
However, the regular attacks would cause moderate damage if they catch an opponent while the Critical and Eclipse attacks would cause massive amounts of damage and knockback. He would swing the Alondite once for the regular attacks and multiple times for the Critical and Eclipse attacks, making him dangerous to be around. This would make sense and be consistent with the strengths and the animations of the attacks from the Fire Emblem series.
You can see all of these attacks in this video (though he slaughters every enemy with one hit regardless):
Start the video at 1:50, where he's using is weapon of choice, the Alondite.
On a side note, he does have his own theme song on the Castle Siege stage and is an item in Smash Tour (big whoop...) But he definitely would have made an awesome assist trophy.
EDIT: Wanted to add my $0.02.
Eggplant Wizard from Kid Icarus would have been fun.
Also, anything from DK. Rambi for example.
Yes, the Donkey Kong series is long overdue to have an assist trophy. And it seems that many people are on the same page when it comes to thinking of Rambi as an Assist Trophy, including me. I figure that as an Assist Trophy, he could run from side to side of the stage he's on and cause damage to opponents by ramming into them, jumping when necessary. But the Gogoat Pokemon sort of already does the same thing though...
This is kind of random, but
Manky Kong would make an obscure yet irritating Assist Trophy to deal with. He'd just stay where he was summoned and constantly hurl barrels until his time expires.
EDIT2: Here's a video. There are two Manky Kongs
from 2:45 to 2:54. (Diddy makes short work of them.)