|Alis suis obumbrábit tibi..||He will overshadow you with His wings.|
Ala,ae = wing. With ‘suis’ (his) this is plural (wings) and could be dative (to/from) or ablative (probably ablative of means).
Tibi = dative, “to / for you.”
Obumbro,are = to conceal, to hide, to defend, to overshadow.
The verb in this sentence is obumbrabit. It is clearly in the future tense. What is the number? Singular. Person? Third. “He will conceal.” This is used with tibi in Luke 1:35, “Spiritus Sanctus superveniet in te, et virtus Altissimi obumbrabit tibi” / “The Holy Spirit will come upon you and the power of the Most High will overshadow you.”
We see this verb (with an accusative) in Luke 9:34 at the Transfiguration: “Hæc autem illo loquente, facta est nubes, et obumbravit eos” / “While he was still speaking, there was a cloud, and it overshadowed them.” So here we have God overshadowing you.
What to do with Alis suis? There are three possibilities: He will overshadow you from His wings; He will overshadow you to His wings; He will overshadow you with His wings. The last is the only real option. He will overshadow you with (by means of) His wings.
How would you say “His wings will overshadow you?” = Alae suae obumbrabunt tibi.
How would you say “They overshadowed us with their wings”? = Ii obumbraverunt nobis alis suis.