I finished the triumph last night in about five hours and had way too many shots of Vodka in the process to make things less boring. All I can suggest is get comfy, put on your favorite film, program or podcast, get drunk and/or high and play in the background like I did.
I definitely think minibosses ought to count. I'm also surprised the Psion engineer doesn't count as it did last year. Anyway, Bungie needs to playtest these things.
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