Vex sacrifices is my favorite public event. If you stray from the conflux they do teleport behind you, but that doesn't mean they can't be taken down. It's wise to save your supers for that, or at least have a Void shotty ready. Btw, popping a polyphage before hand is reason enough to stick around. Those few minutes are pure glimmer.
As far as the Target Eliminations, they are tough and if your flying solo and waiting for that event to complete the bounty, your bound to get frustrated. It's one of those events that really shouldn't be taken on solo.
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Invective and up for anything AR did the charm for me on the moons Target yesterday. Shotguns really did benefit from the buff and after the nerf my fully maxed AR was at least able to Keep his shields down.
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I haven't found the Target Elimination to be tough now (they were tough initially when I was lower level). I just unload everything I have and it's usually OK. Especially now with the shotgun buff in PvE. But the teleporting makes it impossible to complete and it should be fixed.