This is a topic I would like to adress as many need help with trading for GTS legendaries. Let me explain my scenario:
I started on pokemon white and then got X/Y. I have no pokebank, I don't clone, I don't hack and started the GTS trading with three legendaries: Yveltal, Zygarde, and Mewtwo (I still haven't caught my zapdos). As of right now, I have Shiny Mew, Shiny Genesect, Darkrai, Shaymin, Shiny Manaphy, Meloetta, Victini, Jirachi, Keldeo, Arceus, Celebi, Deoxys, Rayquaza, Groudon, Tornadus, Thundurus, Landorus, Giratina, Palkia, Zekrom, Reshiram, Shiny Suicune, Regigias, Heatran, Kyurem, Entei, Raikou, Azelf, Terrakion and counting! (I make around 6 legends profit per day).Not to mention my OU team which includes shiny Charizard, Shiny Scizor, Shiny Metagross, Shiny Poison-heal Gliscor, Shiny Starmie, and Shiny Gengar. Here's how I did it:
Firstly, I started out by testing out what trades well and what doesn't by looking at what people want in exchange (ie. Legends vs starters VS biddof etc.). This is key because it distinguishes Kingdra, a staple in my trading practices, from something like ditto, which is not a staple in my practices. So, Without further adieu, I present to you the staple pokemon that can be traded up to Zapdos (I will explain this later):
See the pattern? All of those need a special item to evolve.
Step 1 to getting the legends you want: Firstly, breed up a bunch of Scythers or Cottonees. It does help to IV breed them, as they trade much faster, but you can still manage without IV breed.
Once finished with a dozen or so, deposit one of them for a one of the above mentioned pokemon. I usually trade up to Kingdra. It usually takes around and hour or two. So be patient (Go outside and see the beauty of nature for a while) . Later, if all goes planned, you should have one of those pokemon. Once obtained, trade the pokemon for a Zapdos. This typically doesn't take too long.
Don't forget about time zones and stuff! In my experience, things trade better at night because where I am (mountain time) night time is around noon for Japan.
Step 2: Good job, You have already crossed the line between non-legend and legend! Well done! Now, take the Zapdos and deposit it for a Xerneas. THis typically takes around 15 minutes, although it can take longer depending on what day it is.
Step 3: Once you have obtained a Xerneas, Deposit it for a Latios. This takes a matter of minutes in my experience. Again, remember that the GTS dies down during the daytime a bit and peaks in the morning and evening!
Step 4: Congratulations! You've made it this far! Now for the easy part! Trade up Latios for Dialga. This takes no time at all. For whatever reason, people must really like Latios...
Step 5: Trade Dialga for any pokemon on the GTS and you should be able to get it in a matter of seconds! Good job! Now you can manage to get any GTS tradable Pokemon. Well done!
Trading up to non-GTS tradable pokemon
Okay, this part is really hard and a lot of work. But as you guys can see, I managed to get every non GTS tradable legendary so bear with me here. In the course of trading up the GTS hierarchy (This is usually after a dozen of legend trades throughout the GTS) You probably managed to obtain a couple shinies of some sort (I get shiny Latios almost 50% of the time). Whenever you find a shiny legend, keep it and save it. That way you can shoutout to everyone "Need Events!" or whatever and then you can trade the shiny legendary for the event you want. THis part is really tricky because you have to initiate trades to passerbys rather than just waiting. In the end, however, you can build your arsenal of legends. Hope this helps everyone!
PS. if you're having trouble, feel free to leave a comment or PM me! Thanks!