The beast of 13:1 is similar to the dragon of 12:3. The dragon had 7 crowned heads and 10 horns, whereas the beast has 7 heads and 10 crowned horns with a blasphemous name* on each head. "...The dragon gave the beast his power and his throne and great authority." (13:2). It seems as if the dragon gets trapped in his own schemes in 12:15-16 and empowers the beast to continue his work.**
Daniel 7:3-6 used the appearance of a leopard, bear and lion as symbols of world power; note the interpretation in Daniel 7:15-28. Thus the beast out of the sea must represent worldly power. He will "exercise his authority for 42 months."***
He will blaspheme God, God's dwelling place and those who live in heaven. Life on earth is likely to be treacherous during this time -- note verses 13:7-10. "...This calls for patient endurance and faithfulness on the part of the saints." (13:10).
*Heads maybe: rulers, kings, presidents, heads of state. Horn symbolizes strength in the Bible; note foot notes on Ezekiel 29:21 and Luke 1:69 for example. Crown symbolizes reward, honor, position or power. Note how crowns shift from the heads of the dragon to the horns of the beast. Does this mean that their reward, honor and power shifts from their position to how they treat people?
Names on the heads: this imagery looks like cartoon characters on the editorial page of a newspaper! Blasphemy in KJ is translated as Evil thoughts in NIV, which in Matthew 5:19 and Mark 7:21 include: sexual immorality, theft, false testimony, murder, adultery, greed, malice, deceit, lewdness, envy, slander, arrogance and folly. It is possible the blasphemous names are related to the 10 commandments. If so, 5 of them would be easy to identify: covetousness, false witness, theft or stealing, adultery, and killing or murder. The other two would be some combination of the first 5 commandments. False God maybe one, which would be similar to the first and second commandments (with 2 horns on this head?). Contempt (disdain or scorn) maybe the other, which would be similar to the third, fourth and fifth commandments (with 3 horns on this head?).
**The beast of 11:7 that kills the 2 witnesses may be the same as in 13:1 and is described more fully in chapter 17. In 12:9 one being has different names. It seems that beast can be added to this list. The different names may describe different aspects or forms of the being, but all seem to have similar attributes, methods and goals. It seems as if Satan can morph himself into just about any form he wishes -- to fool people (often giving people what they think they want) -- only to destroy them in the end.
***It seems the 3.5 years of 13:5 overlap, at least a part of, those of 12:6 and 12:14.