You should kill as many as you can with void beam and AMP. Once all 4 limb is destroyed, Eidolon Teralyst will go down and summon Eidolon Vomvalyst to heal itself. After you find it, you have to repeat the process of depleting it shield, damage it's limb and etc.

After this, it will teleport away which it will do 3 times and again you have to find it and like I said earlier. Run out of the range or simply switch to operator and enter void mode(Crouch) although do note that if your warframe is in the radius, your warfarme energy will be drain. Void mode(Crouch) renders you from it's attack and also if he stomp the ground with his leg(I guess), you simple need to jump at the right time and you will not be knockback.Д«ody emits red color indicating it's limb is vulnerable now.ДЄfter you finish depleting all it's shield(It's shield still can regenerate if it doesn't take damage after a while), it's body will emits red color indicating you can now damage it by damaging it's limb(4 total) and after destroying one of it's limb(Intact Sentient Core will be drop), it will then retaliate by sending energy spike up to 70m away I think and you have 2 option. In doing this, it will try to attack you with it's powerful attacks although it's attack are really predictable and you can easily avoid all it's attacks with the right move. After that you need to take down it's shield which only can be take down using operator void beam and AMP(You get mote amp at first and other craftable from Quills Onkko) which is annoying to be honest but it can be quite quick with good AMP and with teammates. Simply go to it and mark it(Will help your teammates finding him). The first thing you need to do is finding it's spawn location where it will spawn near lake with blue light(Column alike).

There are few phases when you hunt and taking down an Eidolon Teralyst.

How to kill an eidolon