The Europa one would be easiest IMO.
The champion kills in a fireteam counts for matchmade activities (pretty sure), so you can farm cloudstrike and work on that at the same time doing Hero.
Then it’s just clearing up a few odd triumphs to get to 1400.
Pretty much.
Any champion kills you get (and by you, it means you need to get the points up on the screen so make sure you put a few rounds into any champion you see), should count - I’ve got that triumph and I’m a solo player.
Then it’s in the hands of RNG as to the Cloudstrike drop, could need 50 runs, you could get it in 2 🤷
There’s a few triumphs attached to empire hunts too, so if you check what they are you can work on them as well.
Edit: there’s a lot of randomness involved in the Gambit one, and I’m pretty sure some of those weapons only drop from resetting your rank 2 or 3 times (again not 100% on this but pretty sure).