Participating in arena, bridges and you get quite a few from tournament of honour (available from level 16) I think from arena and bridges you only get the lower collections and you can get higher collection pieces from tournament. I've never really paid much attention but I'm sure someone will correct me if I'm wrong.

ellie speaks the truth, arena gets you gladiator trophies, amount of damage increases the likliehood of getting a trophy (or so ive been told) also, tournament of honor gets you higher collections and gladiator rep.
As far the actual piece you recieve, it is random. Best bet is to get to 1k and buy the scheme for converting trophies into the next level up and saving up for big collections :) hope that helps

I only ask casue i keep getting various parts of the shield raiser collection but not the Aegis of Shield Raiser

keep going with it, it will drop eventually :)

Just got a third set of leggings of shield raiser. this is really starting to p*ss me off now

hahah dont worry, i think i ended up with 8 gladiator belts and nothing else at one point :)

Finally got the Aegis. Relief

well done :)