Unfortunately their defensive frailties returned to haunt them at Moss Lane as they had to content themselves with a point despite bagging another goal treble on their travels.
In an entertaining clash between two sides that showed great attacking intent, the Shaymen were in front three times only for Altrincham to hit back on each occasion.
And while two of the Shaymen's goals came from the penalty spot, that should not detract from a performance in which they carved out enough opportunities to have been out of sight by the break.
However, a defence that had conceded one goal in three games, reversed those stats with three goals in one, all of which were entirely preventable.
Town were on the front foot from the start and broke the deadlock after just five minutes.
Gareth Davies played a great ball down the right for Andy Campbell who got the better of Darren Tinson before pulling back for Jon Shaw who stroked home.
Altrincham hit back with a Colin Little shot from the edge of the area that shaved the outside of Adam Legzdins' left hand upright.
But it was a rare Altrincham shot as Town continued to pile men forward at every opportunity.
Davies got Campbell in on the right again and an almost identical pull back for Shaw saw Town's leading scorer denied by home keeper Stuart Coburn.
The resulting corner caused all sorts of chaos in the home defence as Matt Doughty's delivery was played back into the middle by Campbell.
Anthony Griffith met the ball with a downward header that Coburn saved and there were vociferous appeals for a penalty after Campbell's shot from the rebound had struck a defender.
Five minutes later Campbell got away down the left and stuck out a foot to connect with the ball, only for Coburn to parry.
Campbell reached the rebound first and played it across the area for Danny Forrest whose side-footer was heading for the corner of the goal until Tinson thrust out a leg and diverted it behind with his heel.
Despite all their pressure - and chances - Town were pegged back on the half hour when Little somehow found himself unmarked six yards from goal to nod home Ryan Shotton's long throw.
But the Shaymen were back in front four minutes later when Joe O'Neill crashed into Campbell in the area and the striker picked himself up to send Coburn the wrong way from the spot.
Simon Heslop's right foot shot from 18 yards, after he had been picked out by Shaw, forced another good save out of Coburn and all looked rosy again.
But three minutes into the second half, after they had forced a couple of corners, the home side levelled for a second time when Little fired home a penalty after Greg Young was judged to have been bundled over by Jake Wright.
Town almost regained the upper hand three minutes later, Forrest and Shaw combining to release Heslop down the middle, but Coburn saved again.
And Shaw had a shot, from an opening created by Lewis Killeen, blocked behind for a corner by Young.
Legzdins was forced to save from Liam Long who took a Chris Senior pass on his chest before racing into the area and shooting.
But it was Town who struck next, going ahead for the third time in the game from the third penalty - Shaw stroking home his 20th goal of the season after he had been brought down by King.
On this occasion, the Shaymen's lead lasted barely 60 seconds as they failed to deal with a Warren Peyton cross from the left and, after Senior had a shot blocked, Joe O'Neill forced home.
In keeping with what had gone on the opening 66 minutes or so, both sides went for a winner.
O'Neill headed a Chris Lane cross over the top for the home side while Town had a couple of late opportunities themselves.
Campbell had the first when he worked some space for himself on the edge of the area before firing wide while Shaw was denied a hat-trick when his 15-yarder was blocked.

STAR SHAYMAN
Andy Campbell ran the Altrincham defence ragged for 90 minutes last night.
Playing off the last defender, he caused havoc, scoring one goal, after he had been fouled in the area, and setting up the opener.
If only he had not missed such a large chunk of the campaign.
Jon Shaw goes from strength top strength in a Town short with his double at Moss Lane taking him to 20 goals for the season.
But he also work's his socks off to provide the link between midfield and attack as well as getting through a mountain of defensive work high up the pitch.
Gareth Davies has gone quietly about his business since arriving a couple of weeks ago.
While predominantly in the side to defend, he is also a real asset when the Shaymen are going forward and provided Campbell with plenty of chances to get in behind the home side.
Campbell takes the three points on offer in our season-long competition with Shaw taking two and Davies one.

MATCH FACTS
Altrincham: Coburn, Battersby (Lane 46), Shotton, Tinson, Young, O'Neill, King (Roca 88), Lawton, Peyton, Little, Senior (Cahill 85). Subs (not used): Scott, McFadden.
Booked: None
Sent-off: None
Goals: Little 30, 49pen, O'Neill 68.

Halifax Town: Legzdins, Davies, Wright, Clarke, Doughty, Forrest (Nelthorpe 63), Griffith, Heslop, Killeen, Shaw, Campbell. Subs (not used): Mawson, Quinn, Kearney, Harban.
Booked: Wright.
Sent-off: None
Goals: Shaw 6, 67pen, Campbell 35pen

Attendance: 903.
Referee: RJ West (Hull).hy

PLAYER POINTS
Jon Shaw 38, Simon Heslop 32, Tom Kearney 21, Anthony Griffith 21, Andy Campbell 19, Lewis Killeen 14, Steve Torpey 12, Steve Bushell 10, Jake Wright 10, Matt Doughty 9, Daryl Taylor 8, Rob Scott 7, Danny Forrest 6, Adam Legzdins 6, Cortez Belle 5, Craig Nelthorpe 4, Tom Clarke 3, Craig Mawson 3, Nathan Joynes 2, Adam Quinn 1, Darryn Stamp 2, Ryan Toulson 2, Greg Young 2, Peter Atherton 1, Garethj Davies 1

YOU SAY
My word town u score 3 and concede 3. Why cant u defend better? U will need to on saturday coz defending has been poor all season - The Turnbull

Why can't we hold a lead? Northwich,Stafford & Altrincham. Beat none of them. This is the level we have sunk to under Wilder - Jotshan