It's kind of like the Trial of the Sword in that you have to take your time and think strategically, however the main difference here is that you have access to most of your arsenal. If you can stay at a comfortable distance and take enemies down one at a time, you'll do fine.
If you are doing the obliterator challenges, stack up on stamina foods and do glide by bomb arrows, work on getting a 5 shot bow from the strongest lynels for add explosivity.
Make use of items such as majora's mask which can let you get in to the camps and get the lay of the enemies even stealth armor can help you in escaping or sneaking in and stealthstriking, Stasis can be use to show if any sentries are about if they are stasis them then shoot them in the head.
As far as dealing with groups of multiple enemies, my advice is not too. Getting outnumbered was responsible for practically all of my gameovers during this section. Make use of ranged weapons and the environment to separate enemies or pick them off one by one. Only engage with the obliterator in a 1 on 1 situation.
Disengage as soon as you're getting ganged up on and return again when it's settled and you've had chance to scout it out a little.