Chapter 1 of Continuum Turbulence picks up right where the story of Singularity left off, although fortunately the difficulty does not. As is customary for major events, the first Chapter is easily clearable by all Commanders, with requirements starting as low as Level 10 1x linked squads, although by the end of Chapter 1, Commanders will likely need to field level 70 4x squads.
This chapter features a variety of both armored, and unarmored enemies, making an RF/HG based squad valuable during the final maps. The end of this chapter will also be the first to allow for the deployment of Heavy Ordnance Corps, or HOC units. Please see the write-up here for information about HOCs.
The following should be taken as example teams that can be used to clear this event rather than copied as-is; anything that's around the same level will work, provided the team is somewhat built correctly and given equipment.
Level 30 3x Linked
Level 70 4x Linked AR
RF Echelons in Chapter 1 can be used - there's a pretty low barrier of entry. As long as you have some AP ammo and somewhat synergetic HGs, they will work just fine. A little bit of micromanagement/kiting will go a long way.
If you only have a single good RF, perhaps the free Springfield from the new player rewards, you can use a single RF alongside a few buffing HGs and clear fine. Highly-leveled ARs can also brute force the armored units if needed.