Battleborn

As with a lot of these lore challenges, these are probably best won enjoying the game and discovering the character. However, for those that want some tips, this is how I approached completing the challenges. If anybody has any updates or suggestions please let me know. I tended to focus on completing one challenge at a time, whilst trying to chip away at some of the others whenever I could. The order below is the order I approached them in.

My standard Gear loadout for Benedict focused on Reload speed, Cooldown, and Health Regen. I nearly always have a Shard Generator too for all my characters. So for Benedict I had: A Shard Generator, Vyn’s Quiver (20.82% reload; 6.94 Health regen), and Tactical Accelerator (10.50% Cooldown; 9.80% reload).

Complete 3 matches on a team with at least 2 other Peacekeepers
Update: Weasel Pizza has noted in the comments that this IS achievable using Captains Draft and picking two Peacekeepers
I don’t think there’s any easy way to boost this solo; you will need two friends to help. For some of the other “companion” challenges I have been able to split screen but as this requires two I don’t think that is an option. I’ve also tried to pick the PvP Private (against Bots) game type that allows you to select your teammates (PvP Captains Draft) but that doesn’t seem to count towards the progress. You could try getting lucky in a PvP Public (against Humans) as the Peacekeeper characters are quite popular and you might get some legitimate companions, if anybody is playing. Or create a session here on TA.

So once you have two friends have them select either: Galilea, Ghalt, Montana, or Oscar Mike and follow the classic boosting technique for these types of challenges: head into The Algorithm on Hardcore and as soon as the level starts everybody runs outside and jumps off the edge. Repeat three times.

Kill 10 Battleborn while in the air
Given nobody plays online anymore, this is best farmed playing PvP against bots. I would recommend the Incursion game type as this seems to last the full 30 minutes (the other game types can be won quickly sometimes) so this gives you the best chance of making progress. To get this you need to be in the air when you get the final hit resulting in a kill. Because the bots seem to run as soon as their health is low I found the best way was to use Hawkeye (LB button) in tandem. I also found the following helix upgrades useful: Level 1: Persistent Projectiles (RT); Level 2: Wind Chill (RT); Level 3: Ready Rockets (LT); Level 4: Rapid Reload (LT); Level 5: Glide-iator (LT); Level 6: Heavy Bombardment (RT); Level 7: Danger Zone (LT); Level 8: First Class (RT)

I would say that you have your best chance after activating all your gear and getting your Helix to at least Level 6. The technique then is to find a Battleborn target and use your rockets (RT) to drop their shields and health. When they get to about a quarter health use your LB to hit them with a rocket that will activate targeting then hit RB to jump into the air, LT to glide/hover, and finish with a barrage of rockets using RT. Hopefully these should then follow them and finish them, even if they run.

Fire 300 rockets in a single match, 5 times
If you’re as bad a shot as me then you should get this one when playing the PvP for the challenge above. If not, it should be easily boosted by playing any of the PvE campaign levels.

Get 100 kills with Boomsday
I tried to get this one when doing PvP but the bots have quite high health so I ended up farming this using a technique outlined in Goon on Games solution for El Dragon, so all credit goes to them. Fire up The Algorithm and make your way through until you get to Geoff. After you flush him out of the warehouse following his FIRST upgrade he will send infinite minions towards you. I found the best way was to kill the M1 Boom Bots (the ones with the red/green lights) using rockets (RT) then use your Boomsday (Y button) on the M1 Gun Bots (the other bug-like of minions). This was best achieved by running away from the Gun Bots until they were all clumped together and then firing Y. Using rockets on the next wave gave enough time for the Boomsday to cooldown. Equipping Cooldown gear also helps, obviously, but I was able to do this comfortably with my standard Benedict loadout.

Glide for 3,600 seconds
Option 1 (all credit goes to BStringbean in the comments)
I played the Algorithm to farm 100 Boomsday kills, and continued on with the level and found a great spot to farm gliding that seemed to greatly accelerate the time it took. After killing Geoff, continue on with the level and you'll kill another mini-boss, an ice elemental. After that you'll continue down an empty hallway with a checkpoint on your left and leap down a hole. Hold down glide and keep refreshing your RB button power and you'll go down the hole very slowly. Once you reach the bottom, jump in the lava and you'll respawn at the checkpoint above. This method seemed to go way faster than an hour, I only had a little over 10 minutes logged when I started and finished in less than 15 minutes.

Option 2
This for me was the last one to complete, even though I’d tried to incorporate a bit of gliding into all of the other challenges. The best place I could find to boost my gliding was on level 7, The Saboteur. Right at the start of this level you head down a ramp and then directly opposite is a longer, higher ramp.

Kill everything in the area (2-3 enemies) and then glide from each ramp to the other. One is higher than the other so it’s not a straight glide but is the best I could find that didn’t involve a complete climb back to begin another glide. From the top of the taller ramp you should be able to double-jump (double-tap A), hold the left trigger and push forward on the left stick. This will start your glide towards the lower of the two ramps. Whilst gliding, hit the RB button (remember to keep your left-trigger held down) and you will gain some height which should mean you make it to the top of the lower ramp with ease. Turn around and head back using the same technique. On the return trip, try to hit the RB button as early in the glide as possible and this should give you enough Cooldown time to use RB again towards the end of the glide, meaning you very nearly make it to the top of the taller ramp. Run the remainder, turn around and do it all again.

Using this technique I was able to get a good return on glide time against play time and could pretty much get 500 seconds for each 10 minutes of playing.

Equipping extra Cooldown gear also helps but I stuck with my standard Benedict loadout. There are about 900 shards in the immediate area between the two ramps so I would recommend equipping a Shard Generator first then waiting and equipping the Cooldown piece. You can be gliding whilst you wait for the shards to be created.