Chapter 2, Season 8 of Fortnite introduced questlines into Battle Royale, a feature that was in Save The World ever since its release. One of the questlines, Monster Research, is all about experimenting with the Sideways feature that was added this season, with all 5 of the quests offered by Torin, the new Battle Pass character.
Cheat Sheet

The Quests
Enter The Sideways (1)
Accept Dialogue: You think you can handle the Sideways? Prove it.
Guide: The Sideways is a new feature that is randomly generated every match. At the start, a massive bubble will be visible on the Island, which is the gateway to the Sideways dimension. Simply enter it to complete the quest.
Complete Dialogue: Call yourself a hunter if you want, but we’re the ones being hunted.
Reward: 12,000 XP and 20 Bars
Collect A Sideways Weapon (1)
Accept Dialogue: The weapons in there? They’re powerful. I’d grab one, if you can.
Guide: Sideways weapons can be found in chests inside Sideways zones.
Complete Dialogue: Don’t point that thing at me.
Reward: 14,000 XP and 25 Bars
Damage Players With A Sideways Weapon (100)
Accept Dialogue: Sideways weapons have a real kick to ’em. Get used to it.
Guide: While there are AI enemies inside the Sideways, the quest is asking you to deal player damage specifically.
Complete Dialogue: … Maybe you’ll be useful in this hunt after all.
Reward: 16,000 XP and 30 Bars
Eliminate Cube Monsters In The Sideways (10)
Accept Dialogue: This is it. It’s time to prove yourself as a hunter.
Guide: Cube Monsters similar to the ones from Chapter 1, Season 6 pop up in the Sideways, so all you have to do is eliminate 10 of them.
Complete Dialogue: Huh. You survived. Good work.
Reward: 18,000 XP and 40 Bars
Complete A Sideways Encounter (1)
Accept Dialogue: If you can manage a full hunt, I’ll be really impressed.
Guide: Sideways zones can be encountered via purple rifts marked on the map. Completing a full Sideways encounter requires you to eliminate a lot of Cube Monsters, so have a lot of loot with you!
Complete Dialogue: Fine. If you don’t ask any personal questions… you can join my hunt.
Reward: 20,000 XP and 70 Bars