Global 5000 flight crew reported low altitude alert while maneuvering for approach.

Narrative

The captain wanted to take off ZZZ1 runway XX. On the climbout; he elected to clean up the aircraft instead of keeping it slower and intercepting ILS Z Y circle to land 1 into ZZZ. He was going to overshoot the final of runway Y going westbound; so I asked for vectors around to intercept the ILS Z Y again. I make all the appropriate call outs during the intercept and notice he didn't activate the approach on the autopilot. I mentioned that 3 times; but he didn't react or say anything that was intelligible. He overshot the final approach course on heading 090 and 2000'; and then he swung it back on to the final approach course approximately ZZZZZ and then dropped it to 1500' by ZZZZZ1. At ZZZZZ2 (4nm final Runway Y); he was at 1;300'; turned east with heading and speed of 150kts (Vref 112 and Vapp 122kts); and pitched the nose down a bit. We lost a bit of altitude and I was noticing we were getting low. I was about to mention it as ZZZ Tower said 'Altitude Alert 870 feet'. I noticed the hotel pass by his side window (3.5-3.8nm from the threshold of Runway Z); and saw our altitude in the lower 800s before he started pulling up. I readjusted his VS for better vertical guidance as he overshot a quarter mile past the final of Runway Z. He sort of got back on course and somewhat of a glidepath going 145-150 kts at 500' AGL. The surface wind was 320 at 12kts gusting 20kts. He ducked down on short final and very firmly planted the jet at the 500' marker with max reverse and braking applied almost immediately. The jet stopped abeam Taxiway 1 with approximately 400' left on Runway Z. The captain then started a minute one-sided discussion about how he didn't need any help or coaching taxing back Taxiway 2 to FBO X. He was so busy talking about how he didn't need any help that he missed the marshaller; and had to do a 270 degree turn on the ramp to the parking spot. He then blamed me about him missing the marshaller as I maintained my part of the sterile cockpit and made sure he didn't hit the wing taxing in. He was angry and didn't want to talk about it. So I brought the issue and safety report up to company management at a later time.