Having just done this duty myself I can see both sides of the arguement because it is frustrating by design, because that is the intent - it's meant to show
the desperation and confusion the WoL is experiencing in that situation, having had their body stolen by their arch enemy and their soul plonked into a random Garlean centurion which has all the defensive capabilities of a wet paper bag (and the insinuaition is the Garlean whose body you inhabit in that scene was already dead - Maxima tells you afterwards that as soon as your soul vacated it the body went immediately cold and stiff, suggesting you were inhabiting a corpse to boot), and which Zenos proceeds to head to Camp wearing your skin in order to slaughter everyone for the evilz while his insane Ascian sidekick drops you in the middle of the capital ruins again purely for sadistic fun, so your normal way of handling such things is completely thrown out the window.
It is hence best to approach it like the earlier roleplay duty with Thancred, only with even less defensive capability and no actual way of hiding save running for cover.
Hence many aspects of the duty actually reflect this confusion, the timer being the big one - 30 minutes is more than enough time that you need to complete the duty, as the comments to "get to Camp Broken Glass is actually a lie from a gameplay perspective. Your objective is to stay alive and get out of the city - accomplishing that will automatically send you to the camp anyway so it's not an actual rush as much as it seems it is. Having said that, it's still best not to sit around twiddling thumbs so be mindful of the time, but don't let it distract you.
As others have already laid out the strategy, the way to completing is actually quite simple, the hard part is having to skulk around the ruins and wreckage avoiding enemies, although you can afford to kill the occassional soldier,
as Fannyboy so enjoyed mockingly pointing out to you at the start, you simply don't stand a chance against the machina in your Garleansuit
- luckily they're more easily avoided and only seem to be (mostly) in parts of the city where you don't really need to go. This goes for when you find the fuel cannister - if an enemy attacks you while carrying it you will simply drop it and can pick it up again after the enemy is dealt with (this caught me out the second attempt I did it). And where possible, click on the bodies of the dead soldiers scattered around, as they mostly have medkits for healing, a vital means of staying alive. Therefore, the strategy in a nutshell is (possible spoilers):
Right at the start, use Rampart and Fight or Flight (the soldier will not attack you until you attack him, unless you're literally right in his face) then use the weaponskill combo to defeat him. After he's killed, select the 'pay respects' option first, then check his body for a medpack and to satisfy the first requirement which removes the barrier to the next area.
Keep to the ruins and try to avoid enemies if possible, especially the machina (although you probably could take on one of the slashers, the death claws, war machines and iron giants are just too strong and will kill you quickly)
From the starting point head east then south and west, keeping to the walls and wreckage to avoid enemies, this should bring you to a damaged magitek armour that the game will tell you needs to be repaired so as to get rid of all the enemies in front - this involves getting it's key and a fuel cannister.
The key can be found from the wounded soldier lying in a building adjacent to the magitek armour. Speak to him and he'll give you the key.
Double back the way you came, then from the original starting point, keep heading east til you come across another damaged magitek armour that is identified differently to the rest. Click on it to get the fuel cannister that you are now carrying.
Return the way you went, hiding behind rubble and diving through damaged walls and buildings to avoid enemies as much as you can - as stated above if you get attacked you'll drop the cannister, and can pick it back up after fighting the enemy.
Take it back to the magitek armour and once it's activated, climb aboard - it has three attacks, a manual positioning AoE attack that does heavy damage to everything in the AoE, apowerful burst attack that is actually not as useful as it seems, as it only is at close range and has a long cooldown, and a frontal AoE attack that is not as powerful as the burst attack but has a faster cooldown. Use the manual AoE to clear out the bulk of the enemies with the third attack picking off anything that comes in range while the first is cooling down. Once all the enemies are taken care of, you'll be prompted to dismount.
Follow the path beyond that will take you out of the city to underneath a highway overpass where Garlean citizens are fighting random monsters (ice grenades, polar bears and yetis). Help them out as they'll continue to fight if their initial enemy is defeated - just be aware of the ice grenades as they will explode once their HP reaches zero with no visible AoE field and will cause you to take heavy damage.
Eventually they'll reach a point where another Garlean is in magitek armour fighting off more enemies. At a certain point cereleum tanks will drop down and a full area AoE field appears with a small safe zone behind the magitek armour - the pilot will tell everyone to get behind the magitek armour so don't dillydally! A massive explosion will go off that will kill everything, and even knock you down to 1HP (don't worry this is actually scripted)
This sends you into a short QTE where you have to keep yourself from completely blacking out - all you need to do is stop the gauge from reaching zero after ten seconds which is actually easier than it sounds. Just hit the button rapidly and you should pass it (this is probably the easiest QTE I've had to do in the game).
This then leads to the final section where you appear lying on the roadway, and have to crawl a short distance (ignore the 'get to Camp Broken Glass before Zenos and save your friends!' message, you just have to crawl to the end of the street to complete the duty,
which from then on is just cutscene time and once it's all over you'll finally be past this.
So, don't give up hope! It is doable, you just need to approach things with a clear mind and not pannicking.