This time line is derived from Saburo Sakai's reports in Samurai!, Chapters 12-20.

Date Sakai Reports...
13-Mar-42 Japanese troops land at Lae and seize the airfield.
5-Apr-42 4 Zeroes escort 7 bombers to Port Moresby. 2 allied fighters reported shot down with loss of 1 Zero.
6-Apr 4 Zeroes patrol over Port Moresby. 5 allied fighters reported shot down.
7-Apr 2 Zeros intercept 3 allied bombers over Salamaua, shooting down 2; one Zero lost.
8-Apr Saburo Sakai's squadron arrives at Lae, joining two other squadrons that had landed a few days earlier.
10-Apr 6 Zeros escort 7 bombers (Bettys?) to Port Moresby. 2 allied bombers downed while trying to escape. Later, a flight of bombers
11-Apr Sakai's first combat over Port Moresby. 9 Zeros fly over; attack P-39s. 4 P-39s shot down (2 by Sakai).
17-Apr 13 Zeros (6 from Lae on top, 7 from Rabaul in close) escort heavy bombers (Bettys) to Port Moresby. On the way, a flight of P-40s is dispersed. Over Moresby, bombers are jumoed by 6 P-40s; 1, in an extreme power dive, gets a Zero.
19-Apr 7 B-26s hit Lae. They are met by 9 Zeros at 1500 ft. 1 bomber is downed, 1 crippled. Sakai is very angry at the lack of teamwork.
23-Apr Recon over Kairuku (new air field north of Port Moresby), shooting up "carrier planes."
24-Apr 15-Zero strafing raid over Kairuku bags 2 B-26s, 6 P-40s, and probably a P-39.
25-Apr 15-Zero raid over Port Moresby. Met 7 P-40s (6 shot down) for no loasses. Strafing collects 5 B-26s and 2 P-40s.
26-Apr Three of seven P-40s shot down in sweep over Moresby.
29-Apr 7 a.m. raid on Lae by 3 B-17s destroys 5 Zeros, cripples 4. 2 Zeros lift off and chase the B-17s, using all their ammo to shoot down one bomber. 6 Zeros visit Port Moresby at low level, achieving surprise.
30-Apr 5:30 a.m. raid on Lae by 3 B-26s at 600 ft, followed by 12 P-39s strafing Lae, damaging 9 bombers and 3 Zeros. 2 P-39s were shot down.
1-May-42 9 Zeros battled 9 P-40s and P39s over Port Moresby.
2-May 8 Zeros at 18,000 ft bounce 13 allied fighters. 8 allied fighters downed.
3-6-May To Rabaul for RnR leave.
7-May Battle of the Coral Sea, Day 1
4 top Japanses aces fly to Port Moresby. They intercept 10 P-40s in a column, shooting down 7 of them.
8-May Battle of the Coral Sea, Day 2
Fighter sweep over Moresby. Sakai shoots down a P-39.
9-May Fighter sweep over Moresby. Sakai shoots down a P-40.
10-May Patrol over the Coral Sea. Sakai gets a lone P-39.
12-May 15 Zeros near Port Moreseby. Lt. Sasai (Commander of Sakai's Chutai) shoots down three P-39s flying in a column.
13-May 6-Zero recon over Port Moresby is jumped by P-39s.
14-May 7 Zero flight over port Moresby met by P-39s in two and threes flying in all directions (an attempt to better use numbers vs. the maneuverable Zeros.
15-May Rain precludes flight.
16-May Several B-25s make a tree top raid over Lae. No flying for a day and a half until the runway filled in.
17-May Maximum effort fighter sweep: 18 Zeros over port Moresby. 3 "enemy fighter formations" (usually 12 each) clashed with over the air field. 6 P-39s downed. Ota, Sakai, and Nishizawa perform loops over the field at the end of the attack.
18-May 7 Zeros escort 8 Bettys over Port Moresby attacked by 18 allied fighters. 1 Betty, 3 allies shot down..
20-May 15 Zeros over Port Moresby at 30,000 ft. met head on by 10 new version P-39s, with working oxygen. 2 P-39s shot down, but the margin of performance quite narrow at that altitude.
23-May 7 Zeros intercept 5 B-25s at low level over Lae. 1 B-25 shot down.
24-May 11 Zeros bounce 6 B-25s inbound to Lae, shooting down 5.
25-May 4 B-17s attack Lae with 20 fighter escort. Jumped from above by 16 Zeros. 5 allied fighters downed.
26-May 4 B-17s in column with 20 fighters (P-39s) in twos and threes around it intercepted from above by 16 Zeros south of the Owen Stanley mountains. Includes a few chases through mountain passes resulting in the loss of three P-39s.
28-May 5 B-26s hit Lae; 1 downed.
1-Jun-42 13 Zeros from Rabaul plus 11 flying top cover from lae escort 13 bettys over port Moresby. 20 allied fighters defend; 7 shot down. 1 Betty crippled.
2-3-Jun More fighter sweeps over Port Moresby.
5-Jun battle of Midawy announced as a victory, but the pilots at Lae figured something bad had happened as no landing announced.
6-Jun Sakai shoots down 2 raiding B-26s over Coral Sea south of Lae.
7-15 Jun Operational lull over New Guinea, with 1 raid vs. Lae on 9-June. Japanese knew a build up was underway.
16-Jun 21 Zeros catch 3 groups of 12 fighters (newer model P-39s) separated. 19 P-39s shot down. As they return, they catch 10 B-26s raiding Lae (vs. 19 defenders), followed by 10 P-39s strafing. 1 P-39 shot down.
17-Jun 12 Zeros escort 18 bettys to Port Moresby. They intercept 7 fighters and sink an 8000 ton freighter.
18-Jun 9 Zeros and 9 Bettys raid Kido. They are attacked by 10 allied fighters (who lose two).
25-Jun 21 Zeros sweep Port Moresby, shooting down 4 allied fighters.
26-Jun 11 Zeros escort 19 Bettys to Port Moresby. They are met by 12 allied fighetrs; 3 are shot down.
27-Jun Weather changes to rainy season. Rain during the day makes missions impossible for most days. However, the night are clear enough for B-25 and B-26 raids.
2-Jul-42 Heavy raids against Lae (with no fighters available): Low level B-25s, B-26s, and 6 B-17s. No operations possible for 2 days.
4-Jul 21 (angry) Zeros hit Port Moresby. Met by 20 allied fighters (9 shot down). While gone, Lae's fuel dump is hit. As the Japanese returned, another raid by 7 B-26s struck. 1 rammed, 1 shot down in exchange for 1 Zero.
6-Jul 15 Zeros escort 21 Bettys to Port Moresby. 3 allied fighters claimed.
7-10 Jul Lae hit each night.
11-Jul 12 Zeros escort 18 Bettys to Port Moresby; 6 Zeros peel off to attack (but do not kill) 6 B-17s going the other way. 1 Zero shot down. Over Moresby, allied fighters scatter the Japanese.
21-Jul Japanese land at Buna, 110 miles south of Lae along the coast. The Lae wing's orders change from attacks on Moresby to providing air cover over the beachhead. The Japanese also land at Rabi, on the eastern point of New Guinea and build a fighter strip. However, this is seized a few days later and quickly occupied by allied air units. Other airstrips are built at other forward locations.
22-Jul 6 Zeros were patrolling at somewhat under a 7,000 cloud ceiling, when an explosion from nowhere shook the Buna ammo dump. Sakai spotted a "Hudson" bomber that performed well dogfighting against the Zeros. The Zeros also hit upon 5 P-39s at low level.
26-Jul Sakai's last mission to Port Moresby, after a running chase of 5 B-26s ( 2 were shot down).
29-Jul The Buna patrol reports contact with US naval aircraft: SBDs, F4Fs, with P-39 guides (claimed 3 SBDs, 5 F4Fs and a P-39 downed). They all found this disconcerting - that the USN could afford to send a carrier to the Coral Sea so soon after Midway.
30-Jul 9 B-17s attack Buna with "considerable success." 1 B-17 is shot down.
2-Aug-42 At 12,000 ft over Buna, a 9-Zero patrol met head-on with a 5 B-17 raid. The Zeros attack head-on in column, shooting down all the B-17s (2 explode ferociously). The Zeros also shoot down 3 P-39s trying to support the B-17s. 1 Zero lost.
3-Aug Most of the fighters withdrawn to Rabaul. The pilots believed it was a temporary reassignment.
4-7 Aug Flew recons and fighter sweeps over Rabi.
8-Aug 18 Zeros and 27 Bettys fly 1120 mile range attack on Guadalcanal from Rabaul. Sakai was wounded in the arm and lost an eye. The rest of the Lae fighter Wing remained at Rabaul.

I suspect that the "Lockheed Hudson bomber" was an A-20C Havoc, since Hudsons were generally not armed with any forward guns and were not used as general bombers, whereas this aircraft had multiple guns about its nose, was capable of some spectactular aerobatics, and a good press of speed.