Here is the sentence - My background reflects the ability to take multiple tasks to completion accurately and in a timely manner.

My question, do I need a comma after completion?

It seems to me to be an awkwardly phrased sentence. This would be smoother:

My background reflects my ability to complete multiple tasks accurately and in a timely manner.

(No comma needed in either sentence.)

Further...! Even better phrasing would be this:

My background reflects my ability to complete multiple tasks accurately and quickly.

The phrasing "accurately and in a timely manner" is not good because it's not parallel; that is, you should have two adverbs or two prepositional phrases, not one of each.

http://grammar.ccc.commnet.edu/grammar/parallelism.htm

To determine if you need a comma after "completion" in the given sentence, let's examine the structure of the sentence. In this case, "to take multiple tasks to completion accurately and in a timely manner" is a descriptive phrase that provides additional information about "My background."

To decide whether a comma is required, you can apply the general rule for using commas in a series. When you have a series of three or more items or phrases joined by coordinating conjunctions (such as "and"), it is common to use a comma before the coordinating conjunction.

In this sentence, "accurately and in a timely manner" are two descriptive phrases that are joined by the coordinating conjunction "and." Since there are only two phrases in the series, it is not necessary to use a comma before "and." Therefore, in this case, you do not need a comma after "completion" in the sentence.

Corrected sentence: "My background reflects the ability to take multiple tasks to completion accurately and in a timely manner."