Complicated Conditional Formatting based on 2 Tables

Can you upload an example of how your data is laid out? (Go Advanced>Manage Attachments)

I don't think you can use Table column references in Conditional Formatting (I may be wrong about that)
But you should be able to just by referencing columns.
To just look at the time, in history
=MOD(A2,1) will remove the date in your formula.

Okay, this is better. Now,

Is there anyway I could highlight an entire row in MONITORDATA when the HISTORY[MODE] = "ALM" BUT, only if HISTORY[MEMORY] = MONITOR DATA[MEMORY, the times are also equal.

Table 1 (MonitorData) has 109 rows and 2 (History) has 106. Would they normally have the same # of rows?

Are you looking at Cycle Time as one of the times to compare? If not, then what? Cycle time is not a real time, you'll need to convert them.
There is no "Memory" header on your MonitorData Table.

Okay, I found the time column (DB). There is still no MEMORY column so don't know how I can compare the two MEMORY Columns.
Also, your time in HISTORY is text. To fix this, change your formula to =RIGHT(A5,5)+0

The CONDITIONAL Formatting Formula you are looking for (I could do better if I could find a MEMORY Column I am assuming it is De ("Memo #") is

Select your entire Table 1 (no headers), Conditional formatting> New rule

=AND(Sheet1!$E5="ALM", Sheet1!$F5=$DB7, $DE7 = Sheet1!$C5)