One of the things I love about Demigod is that there are so many ways to use each Demigod, and a lot of technique to using each ability. Why do I bring this up? In this build, we are going to skip Snipe completely, or at least put it off until late-game. I know that sounds crazy, but even though it's a great finisher, and it can turn the tide of a battle going on far away, it's not a great ability if the fight is happening anywhere near you. It's a good power, and I've seen great Snipe Regulus builds do just as well, but for those who prefer to kill someone before they even know what hit them while maintaining high DPS, try this out and you might not want to take Snipe ever again.
Equipment
This is an ability spam build, so it is extremely mana-heavy. You can either get a favor item that helps this out, or you can get health to alleviate Reg's main weakness (you still have to run a lot either way). I personally use Blood of the Fallen. For standard equipment, prioritize +mana and +weapon damage. Avoid +Attack Speed % until late game since you will be using Angelic Fury, and you will drain your much-needed mana pool too quickly. At the start I don't even get any potions, I just buy damage gloves and a sacred helm.
Leveling Plan (Levels 1-6).
Level 1. Get Angelic Fury. It will level you up FAST and give you a nice +25 weapon damage per level (each level after does not increase mana cost). For items, I initially don't buy any potions or teleport scrolls, I buy a Sacred Helm and Gauntlets of Brutality. Combined with Angelic Fury, that's +50 weapon damage before the game has even started. Ideally, you want to leave AF on 24/7 (don't get the final level). You should be mowing creeps down like nobody's business, and other Demigods will be flabbergasted at how fast you're killing them with nothing but DPS.
Level 2. Get Sniper Scope. You'll need all the range you can get as Regulus, but of all your abilities, this takes the least priority from here on out. You only need this first one now since his range is so pathetically short to start. The level 1 scope upgrade, firstly, allows you to shoot towers in safety, and second, allows you to shoot enemy Demigods who think they're safe when they retreat right next to their towers. You would not believe how many stand in front of their towers instead of behind them, which is logically within your safe firing distance.
Prioritize killing reinforcements at this early stage, capping flags as necessary. If you see an opportunity to kill an enemy DG, take it, but take care not to overextend yourself, as Regulus is squishy as hell. Your goal is to level up quickly, because this build is a relatively late-bloomer, although it's good enough in the lower levels that you don't feel like you're sacrificing anything. Hell, the DPS alone is more than enough to get easy DG kills at level 1.
Level 3. Get Mines I. This is more of an investment than a power pick. Mines I is quite poor.
Level 4. Get Mines II. Now we're getting somewhere. Mines II costs just a small bit more mana than level 1, but sets two mines, and both do more damage than level 1 mines. This makes setting traps a lot easier, and it's the first level of Mines you can realistically use as Grenades.
Level 5. Get Mark of the Betrayer. I know I called this the Mine-Grenade strat, but MotB is the crown jewel that makes the whole thing work. It does HUGE damage, has a near-instant cast time, and has a massive slow attached to it. It costs loads of mana, though, and has a long cooldown. Combine this with Mine Grenade tactics and you can take a Demigod from full to almost-dead in no time flat. Use this ability first thing anytime you see an enemy Demigod in range. It's especially devastating against Generals.
Level 6 and Beyond: For as long as this strat works, prioritize upgrading your powers like this: MotB > Angelic Fury > Mines > Sniper Scope/Maim/Snipe (whichever one you choose depends on the situation and your preference, but pick one and only one). You want Angelic Fury more than Mines because even though mines are REALLY good burst damage, each Angelic Fury level is a free +25 weapon damage, without costing extra mana per shot, which does LOADS for your DPS, mana efficiency, army-killing potential, and leveling speed. Your goal now should be to kill reinforcements and blow up their buildings, killing DGs as opportunities arise, and if this requires you to spend money on new reinforcement types (Priests, Angels, Catapultasaurii, Giants), do so. They are a great investment. Priests not only do good damage, they will even heal you if you're nearby, so they can save you in a pinch. Catapults are devastating attackers with a lot of range, and Giants just rock (HAWHAWHAW I MADE A FUNNY).
From here on out, it's pretty self-explanatory. This build is EXTREMELY MANA-HEAVY, particularly if you want to fight Demigods, so you'll probably be spending a lot of gold on mana potions. I usually don't carry health potions except for rare occasions, because your burst damage will be so high that you can survive completely off of health dropped by dead DGs. If you want to be extra-safe, though, don't forget that the Artifact shop sells better combat potions than the base shop.
General Tactics
-DO NOT DIE! You almost completely stop receiving gold income, and you give the enemy team a ton of xp and gold. If you start getting attacked by an enemy Demigod, and you're not ABSOLUTELY SURE you can kill him first, run to the safety of your towers and take potshots at him when opportunities present themselves. DO NOT CHASE PEOPLE INTO THEIR BASE UNLESS YOU HAVE LOTS OF HEALTH AND HE WILL DIE IN A MAXIMUM OF THREE HITS! Obviously, do not chase if you're too slow to shoot him on the move. Take into account the fact that most people may buy a health potion, too!
-Don't feel bad if you need to run away. Just because you retreat doesn't mean the battle is lost. Regulus thrives off hit-and-run tactics.
-Try as best you can to team up with friendly Demigods. Assists are fantastic sources of gold and exp for the whole team. I'm pretty sure it doesn't matter how many people assisted the kill, everyone that assists always gets half the gold and exp that the killer receives, while the killer does not receive less of either, so it's better if the whole team works together to bring down other Demigods. For farming reinforcements, stick to your own lane, but for Demigods, do whatever you can to help out without killstealing.
-You still want at least 2 Teleport scrolls: one to get back to fighting, then another when you need to spend your money again.
-If your war rank is 3 or more, buy the Currency upgrade. This makes a HUGE difference, and it means your whole team will be able to afford more of everything in the future. Seriously, the first level just about doubles your whole team's base income.
Mine Tactics
Few people realize how versatile mines are until they get instagibbed 5 times in a row in ways they never imagined...or you're the one doing the instagibbing. 
Mine-Grenades: Simply throw mines at where you expect the enemy to be when they land. The enemy won't have time to get away before they go off, and you'll do a TON of damage. 1/2 to 3/4 their health depending on the Demigod and the level of your Mines skill. The tricky part is leading your target properly, but with practice you can reliably nail people. They don't have to hit the first time to be useful, though. Not only is the blast radius larger than the detonation radius (NPCs can set them off and hit Demigods), but sometimes your enemy just forgets about them and steps on them anyway. This is great against Generals, since it kills any minions they might have nearby.
It's a Trap! Throwing them behind an enemy DG means he has to commit to the battle. If he tries to run, he either has to go all the way around, giving you many free shots, or he trips your mines and dies anyway. Obviously, this assumes he doesn't have a teleport item. This usually isn't a great idea unless he was already hurt before you showed up, though, because even with HP items, Regulus is squishy as hell. That's what situational awareness is for.
Stay back! I've got a bomb! Throw mines at your feet so that any meleers are punished when they try to slap you. They can trigger when reinforcements try to melee you, so avoid this near creep lanes.
Screw you guys, I'm going home. Throw mines behind you before the fight starts, so if the fight turns south, you have a contingency plan: either you safely get away, or you end up killing the enemy DG as he tries to chase you down.
With a bit of planning, you can even do two of the above.
Next time yeh'll bloody ASK before you stand on MY point! If you see flags that reinforcements don't run through, set mines on the enemy side so that they'll think twice before capping it next time. Usually they won't have a chance to get away with 300 health left if you're nearby (or you teleport in with a warp scroll), and if you used Shrapnel Mines, they're trapped for sure by the 30% slow per mine. If you managed to sneak Snipe in there, you're guaranteed a kill.
The BFG9000! Oh, yes. If you get surrounded by powerful reinforcements, a General is nearby and you need to hit him and his minions all at once, or you just want to see a lot of things die RIGHT NOW, throw a few mines in the middle of the horde and watch as they all go flying off the map...hopefully damaging any Demigods nearby. Sometimes it results in a Double Kill.
lol u c wut i did thar? When an enemy DG starts teleporting in via scroll, you will be able to see the effect, and I'm sure you'll know what they look like by now. Throw mines at the spot (not too close to the building or it'll trigger them early), and right as they land, they take 3 mines to the face.
I GOTTA PRESENT FOR YA. Throw mines at towers. They trigger off the towers, and will do massive damage. Anyone who's played C&C will get the reference. 
This strat has served me well in the pantheon. Most players don't even know what killed them. It almost seems overpowered when you see how fast you kill other Demigods. Don't get cocky, though. The greatest counter to this strat is your own overconfidence. Regulus can't last very long in combat, so if you start getting hit, it's probably time to start running. I hope this serves anyone who wants an unconventional build well. It's done wonders for me. 