First, you must complete the smaller tournaments before unlocking the big tournaments. Once you have unlocked the larger challenges, select The Gully. There are a few ways to earn the trophy.
1) Solo. Grind it out for hours fighting enemies equal to your level.
2) Co-op. Have your main character be a low level (10-20) and your second a high level (50+). Have the low level character start up the larger tournament for The Gully and use your high level character to kill enemies. This is the safer method compared to playing solo.
3) Online. Jump in a game that is playing in this tournament. You only need to be present for the last wave of the last round in order to unlock the trophy.
Once you have completed the tournament, the trophy will unlock. A few tips for The Gully are as follows:
Pick off eridians that fire mortar flames as this can be vital when fighting other enemies and/or trying to heal.
For herding the horde wave to where they cannot attack you, jump on the highest rocks located in the high camp (see video at 3:21).
For difficult bosses, stay at the high camp and pick them off until they come up to you. If the reach you before you kill them, drop down below and pick them off from there. Rinse and repeat.
Playing with no shield is by far the worse handicap. If this happens, make sure to play with extreme caution as you will certainly be killed a lot faster.
Here is the video reference mentioned above. Credit goes to DnB Alex.
Happy Hunting :)