If I wanted to do what you describe, here's how I would proceed, based on one sprinkler at a time, with all sprinklers identical.
1) Pick a place to tie in to the existing supply for irrigation. Could be chosen for proximity and convenience and having some part of the step (2) plumbing already done; or could be chosen to be as upstream as possible to minimize pressure loss upstream of the tie-in point. Location could be reevaluated based on the initial calculations.
2) Stub up a riser with a pressure gauge (could be a hose bibb for a hose bibb pressure gauge) and a downstream ball valve. [The optimal geometric arrangement of the pressure gauge and the ball valve to minimize dynamic effects on the pressure measurements is not something I know, and is something I would like to know. My understanding is that the effects are not large, but I'm not 100% on that.] Measure the static pressure (no flow). Open the ball valve and measure the flow rate (how long to fill up a calibrated 5 gallon bucket) and the residual pressure on the gauge. These numbers characterize the water supply available at that point.
3) Determine the sprinkler model to be used and its specification for flow rate and required pressure at the sprinkler at that flow rate for design operation. Smaller numbers are easier to make work (smaller pipe sizes required), e.g. 5 gpm @ 20 psi is a lot easier than 10 gpm @ 40 psi. [A further optimization might be to use more frequent sprinklers with a lower demand near the end of each branch, with larger sprinklers with a higher demand closer to the source.] Based on the numbers from (2), determine the residual pressure at the tie-in point for the design flow of one sprinkler. [Calculation details omitted for now, but you could confirm the calculation by throttling the ball valve until the flow rate matches the sprinkler design flow, and measuring the residual pressure.]
4) Relative to the location in part (2), determine the elevation of each sprinkler location. Convert those elevations to psi (2.3' = 1 psi). Associate to each sprinkler a psi budget for frictional losses: the residual pressure from (3) - sprinkler required pressure from (3) - elevation in psi. Where the budget is at least, say, 5 psi, you could supply those sprinklers without a pump. Where it's less than 0 you need to use a pump (or if close to zero, switch to a sprinkler with a lower psi requirement for the design flow). Between 0 and 5 psi, it's possible without a pump, but you might need to use a really big pipe size.
5) So consider first a totally level branch. Based on the distance to the end of the branch, and the residual pressure, and the type of pipe you want to use (from what I gather here, probably a 100 PSI - 200 PSI rated poly would be typical), and the particular ID of that pipe for the various nominal sizes, determine the size pipe you need so that the frictional losses at the design sprinkler flow for that length and ID do not exceed the psi budget. [See the calculator posted earlier.] For this case you can run the resulting size pipe along with an electrical conduit for sufficiently large wires for a solenoid valve for your sprinkler, so that a central controller can alternate the sprinklers for you.
6) Now you mention one branch goes downhill at the end; that works to your advantage. Your psi budget at the end is larger than if the branch were level, but after you size the pipe based on the end, you should double check the higher up sprinklers until you get back to level. They will have lower psi budgets, but the distance from the source will be less. You also need to check the static psi at the low point of the branch (just the static measurement from (2) plus the elevation loss in psi) and be sure your pipe is rated at least that many psi.
7) Lastly for the uphill branch it sounds like you will have sprinklers with a negative psi budget. Say the lowest number is -50 psi. I would think +20 psi would be a good minimum budget for pipe sizing (you could go higher). That means you would need a pump that can add 70 psi while passing the design flow rate of one sprinkler. [I know very little about how to pick a pump, but that's the key criterion for the design.] Simplest would be to add the pump at the start of that branch. Then for the actual pump you pick, determine the psi added at the sprinkler design flow rate (should be at least 70 psi for this example). Add that psi to the psi budget of all the sprinklers downstream of the pump. Now you can again size the pipe for the branch based on the psi budget and distance to the end sprinkler, assuming that's the highest sprinkler and will therefore control the design. Your pipe will need to rated for the static pressure at the pump location plus the maximum pressure the pump can generate plus a safety margin.
Cheers, Wayne
